finite horizon markov decision processes with uncertain terminal payoffs this paper deals with the problem of finding an estimate of the maximal loss of optimality which can arise when terminal payoffs are uncertain and policies are restricted in some way the original non convex optimization problem is converted to a sequence of sub problems involving the maximization of a bilinear function over a convex region the paper deals solely with the theoretical issues

a reconstruction theorem for genus zero gromov witten invariants of stacks we generalize the first reconstruction theorem of kontsevich and manin in two respects first we allow the target space to be a deligne mumford stack second under some convergence assumptions we show it suffices to check the hypothesis of h 2 generation not on the cohomology ring but on an any quantum ring in the family given by small quantum cohomology as an example the latter result is used to compute genus zero gromov witten invariants of p 1 b

openness of versality via coherent functors we give a proof of openness of versality using coherent functors as an application we streamline artin s criterion for algebraicity of a stack we also introduce multi step obstruction theories employing them to produce obstruction theories for the stack of coherent sheaves the quot functor and spaces of maps in the presence of non atness

brauer groups and quotient stacks a natural question is to determine which algebraic stacks are quotient stacks in this paper we give some partial answers and relate it to the question of whether for a scheme x the natural map from the brauer group equivalence classes of azumaya algebras to the cohomological brauer group the torsion subgroup of h 2 x inline graphic xmlns xlink http www w3 org 1999 xlink xlink href 01i m is surjective

the period index problem for fields of transcendence degree 2 using geometric methods we prove the standard period index conjecture for the brauer group of a field of transcendence degree 2 over fp

compactified picard stacks over the moduli stack of stable curves with marked points abstract in this paper we give a construction of algebraic artin stacks endowed with a modular map onto the moduli stack of stable curves of genus g with n marked points the stacks we construct are smooth irreducible and have dimension 4 g 3 n yielding a geometrically meaningful compactification of the universal picard stack parametrizing n pointed smooth curves together with a line bundle

moduli spaces of hyperelliptic curves with a and d singularities we introduce moduli spaces of quasi admissible hyperelliptic covers with at worst a and d singularities the stability conditions for these moduli spaces depend on two rational parameters describing allowable singularities for the extreme values of the parameters we obtain the stacks of stable limits of a n and d n singularities and the quotients of the miniversal deformation spaces of these singularities by natural mathbb g m actions we interpret the intermediate spaces as log canonical models of the stacks of stable limits of a n and d n singularities

weak approximation for isotrivial families we study weak approximation for isotrivial families of rationally connected varieties over a smooth projective curve in the case where the family is formed by taking a quotient of a cyclic group action we find a necessary and sufficient condition for weak approximation to hold in most other cases there is also a sufficient condition we also check that this condition is satisfied for all smooth fano hypersurfaces in projective spaces

cohomology and base change for algebraic stacks we prove that cohomology and base change holds for algebraic stacks generalizing work of brochard in the tame case we also show that hom spaces on algebraic stacks are represented by abelian cones generalizing results of grothendieck brochard olsson lieblich and roth starr to accomplish all of this we prove that a wide class of relative ext functors in algebraic geometry are coherent in the sense of m auslander

a stopping rule for forecast horizons in nonhomogeneous markov decision processes we formulate a mixed integer program to determine whether a finite time horizon is a forecast horizon in a nonhomogeneous markov decision process we give a bender s decomposition approach to solving this problem that evaluates the stopping rule eliminates some suboptimal combinations of actions and yields bounds on the maximum error that could result from the selection of a candidate action in the initial stage the integer program arising from the decomposition has special properties that allow efficient solution we illustrate the approach with numerical examples

finite horizon semi markov decision processes with application to maintenance systems abstract this paper investigates finite horizon semi markov decision processes with denumerable states the optimality is over the class of all randomized history dependent policies which include states and also planning horizons and the cost rate function is assumed to be bounded below under suitable conditions we show that the value function is a minimum nonnegative solution to the optimality equation and there exists an optimal policy moreover we develop an effective algorithm for computing optimal policies derive some properties of optimal policies and in addition illustrate our main results with a maintenance system

on proper coverings of artin stacks abstract we prove that every separated artin stack of finite type over a noetherian base scheme admits a proper covering by a quasi projective scheme an application of this result is a version of the grothendieck existence theorem for artin stacks

epsilon dominating solutions in mean variance portfolio analysis abstract in this paper the problem of finding the effcient set of portfolios in a general constraint set is replaced by finding a set of epsilon dominating protfolios the number of which is determined by the size of epsilon algorithms and associated theory are given together with some possible modifications

tautological classes on the moduli spaces of stable maps to p r via torus actions we present a localization proof of the fact that the cohomology of the moduli spaces of genus zero stable maps to projective spaces is entirely tautological in addition we obtain a description of a bialynicki birula decomposition of the stack of stable maps in the context of gathmann s moduli spaces of maps with prescribed contact order to a fixed hyperplane we show that the decomposition is filterable

technical note identifying forecast horizons in nonhomogeneous markov decision processes a procedure for identifying forecast horizons in nonhomogeneous markov decision processes based on convergence results for relative value functions is developed two different algorithmic implementations of this procedure are discussed and a closed form expression for computing sufficiently long horizons to guarantee epsilon optimality is presented

duality theorems for etale gerbes on orbifolds abstract let g be a finite group and y a g gerbe over an orbifold b a disconnected orbifold y and a flat u 1 gerbe c on y is canonically constructed from y motivated by a proposal in physics we study a mathematical duality between the geometry of the g gerbe y and the geometry of y twisted by c we prove several results verifying this duality in the contexts of non commutative geometry and symplectic topology in particular we prove that the category of sheaves on y is equivalent to the category of c twisted sheaves on y when y is symplectic we show by a combination of techniques from non commutative geometry and symplectic topology that the chen ruan orbifold cohomology of y is isomorphic to the c twisted orbifold cohomology of y as graded algebras

nonclassical fields with singularities on a moving surface fields with singularities on a moving surface s with boundary s can be represented as distributions which have their support concentrated on s and s this paper considers such fields of the form f f s where f is the distribution determined by a field f and s is a dirac delta distribution with density concentrated on the tube s swept out by the moving surface a straightforward calculation of the distributional gradient curl divergence and time derivative of such fields yields fields of the following general form g g s s n s the density is shown to contain all the information which is customarily presented in the jump conditions for fields with singularities at a moving interface examples from electromagnetic field theory are presented to show the significance of the other terms g s and n s

the hilbert stack let x s be a morphism of algebraic stacks that is locally of finite presentation with affine stabilizers we prove that there is an algebraic s stack the hilbert stack parameterizing proper a

stable points on algebraic stacks abstract this paper is largely concerned with constructing coarse moduli spaces for artin stacks the main purpose of this paper is to introduce the notion of stability on an arbitrary artin stack and construct a coarse moduli space for the open substack of stable points also we present an application to coherent cohomology of artin stacks

monoidal infinity category of complexes from tannakian viewpoint in this paper we prove that a morphism between schemes or stacks naturally corresponds to a symmetric monoidal functor between stable infty categories of quasi coherent complexes it can be viewed as a derived analogue of tannaka duality as a consequence we deduce that an algebraic stack satisfying a certain condition can be recovered from the symmetric monoidal stable infty category of quasi coherent complexes with tensor operation

dirac tensor distributions for moving submanifolds of rn this paper considers nonclassical fields tensor distributions of the form where is the dirac delta function for a moving p dimensional submanifold of rn 0 p n the density is a classical smooth rank k tensor field on rn 1 the main result of the paper is the development of formulas for the distributional derivatives of such fields the derivatives considered are the absolute differential levi civita connection the covariant derivative along a given vector field the divergence operator the exterior differential and the exterior codifferential the resulting derived fields are shown to reflect the underlying geometry of the submanifold as well as the nature of its motion in the special case p n it is seen that the jump conditions on fields at the boundary of the region arise naturally from the distributional calculus

noetherian approximation of algebraic spaces and stacks we show that every scheme resp algebraic space resp algebraic stack that is quasi compact with quasi finite diagonal can be approximated by a noetherian scheme resp algebraic space resp stack more generally we show that any stack which is etale locally a global quotient stack can be approximated examples of applications are generalizations of chevalley s serre s and zariski s theorems and chow s lemma to the non noetherian setting we also show that every quasi compact algebraic stack with quasi finite diagonal has a finite generically flat cover by a scheme

cycle groups for artin stacks we construct an algebraic homology functor for artin stacks of finite type over a field and we develop intersection theoretic properties

minimum risk probability for finite horizon semi markov decision processes abstract this paper studies the risk probability criteria for finite horizon semi markov decision processes the goal is to find an optimal policy with the minimum risk probability that the total reward produced by a system during a finite horizon does not exceed a reward level where the optimality is over the class of all randomized historic policies which include states planning horizons and also reward levels under mild conditions the optimality equation and the existence of optimal policies are established and in addition an iteration algorithm for solving optimal policies is developed our main results are applied to a manufacturing system

gromov witten theory of deligne mumford stacks given a smooth complex deligne mumford stack cal x with a projective coarse moduli space we introduce gromov witten invariants of cal x and prove some of their basic properties including the wdvv equation

chern classes of deligne mumford stacks and their coarse moduli spaces let x be a complex projective algebraic variety with gorenstein quotient singularities and mathcal x a smooth deligne mumford stack having x as its coarse moduli space we show that the csm class c sm x coincides with the pushforward to x of the total chern class c t i mathcal x of the inertia stack i mathcal x we also show that the stringy chern class c str x of x whenever it is defined coincides with the pushforward to x of the total chern class c t ii mathcal x of the double inertia stack ii mathcal x some consequences concerning stringy orbifold hodge numbers are deduced

simultaneous semi stable reduction for curves with ade singularities a key tool in the study of algebraic surfaces and their moduli is brieskorn s simultaneous resolution for families of algebraic surfaces with simple du val or ade singularities in this paper we show that a similar statement holds for families of curves with at worst simple ade singularities for a family x b of ade curves we give an explicit and natural resolution of the rational map b 99k mg moreover we discuss a lifting of this map to the moduli stack mg i e a simultaneous semi stable reduction for the family x b in particular we note that in contrast to what might be expected from the case of surfaces the natural weyl cover of b is not a sufficient base change for a lifting of the map b 99k mg to mg

the maximization of a function over the efficient set via a penalty function approach abstract in this paper we present several equivalent mathematical programming formulations of the problem of maximizing a function over the efficient set in the case of a polytopal feasible region and linear functions penalty function formulations and their properties are given an examination is made of computational aspects epsilon efficiency the appropriateness of the original problem formulation and of nonlinear extensions

p adic l functions and the coniveau filtration on chow groups we give evidence for the refined version of the bloch beilinson conjecture involving coniveau filtrations by studying several infinite families of cm motives indexed by the integers r 1 that are irreducible of hodge type 2r 1 0 0 2r 1 and whose l functions vanish at the center in each case we construct a corresponding algebraic cycle that is homologically trivial but nontrivial in the top graded piece for the coniveau filtration consequently we obtain new explicit examples of cycles that are nontorsion in the griffiths group the proof of the main result relies crucially on p adic hodge theoretic methods and in particular on the relation between images of homologically trivial cycles under the p adic abel jacobi map and the values of p adic l functions

extending families of curves over log regular schemes in this paper we generalize to the log regular case a result of de jong and oort which states that any morphism satisfying certain conditions from the complement of a divisor with normal crossings in a regular scheme to a moduli stack of stable curves extends over the entire regular scheme the proof uses the theory of regular log schemes i e schemes with singularities like those of toric varieties due to k kato 9 we then use this extension theorem to prove that under certain natural conditions any scheme which is a successive fibration of smooth hyperbolic curves may be compactified to a successive fibration of stable curves 1991 mathematics subject classification primary subject 14h10 secondary subject 14e15

functorial reconstruction theorems for stacks abstract we study the circumstances under which one can reconstruct a stack from its associated functor of isomorphism classes this is possible surprisingly often we show that many of the standard examples of moduli stacks are determined by their functors our methods seem to exhibit new anabelian style phenomena in the form of structures in the category of schemes that encode automorphism data in groupoids

a luna etale slice theorem for algebraic stacks we prove that every algebraic stack locally of nite type over an algebraically closed eld with ane stabilizers isetale locally a quotient stack in a neighborhood of a point with a linearly reductive stabilizer group the proof uses an equivariant version of artin s algebraization theorem proved in the appendix we provide numerous applications of the main theorems

gromov witten gauge theory we introduce a modular completion of the stack of maps from stable marked curves to the quotient stack pt c x and use this stack to construct some gauge theoretic analogues of the gromov witten invariants we also indicate the generalization of these invariants to the quotient stacks x c x where x is a smooth proper complex algebraic variety

stable logarithmic maps to deligne faltings pairs i we introduce a new compactication of the space of relative stable maps this approach uses logarithmic geoemetry in the sense of kato fontaineillusie without taking expansions of the target the underlying structures of the stable logarithmic maps are stable in the usual sense

foncteur de picard d un champ algebrique resume in this article we study the picard functor and the picard stack of an algebraic stack we give a new and direct proof of the representability of the picard stack we prove that it is quasi separated and that the connected component of the identity is proper when the fibers of x are geometrically normal we study some examples of picard functors of classical stacks in an appendix we review the lisse etale cohomology of abelian sheaves on an algebraic stack

finiteness theorems for the picard objects of an algebraic stack abstract we prove some finiteness theorems for the picard functor of an algebraic stack in the spirit of sga 6 exp xii and xiii in particular we give a stacky version of raynaud s relative representability theorem we give sufficient conditions for the existence of the torsion component of the picard functor and for the finite generation of the neron severi groups or of the picard group itself we give some examples and applications in appendix a we prove the semicontinuity theorem for a non necessarily tame algebraic stack

the witten equation mirror symmetry and quantum singularity theory for any nondegenerate quasi homogeneous hypersurface singularity we describe a family of moduli spaces a virtual cycle and a corresponding cohomological eld theory associated to the singularity this theory is analogous to gromov witten theory and generalizes the theory of r spin curves which corresponds to the simple singularity ar 1 we also resolve two outstanding conjectures of witten the rst conjecture is that ade singularities are self dual and the second conjecture is that the total potential functions of ade singularities satisfy corresponding ade integrable hierarchies other cases of integrable hierarchies are also discussed

jump conditions for fields that have infinite integrable singularities at an interface jump conditions are derived for a basic set of first order partial differential equations whose fields have infinite integrable singularities as well as finite discontinuities at a moving and deforming interface these basic formulas are then applied to maxwell s electrodynamic equations and yield the jump conditions that hold when the electric and magnetic fields have such singularities these jump conditions are shown to be generalizations of formulas previously derived for double charge layers in electrostatics and for an interface with surface magnetization density in magnetostatics the basic formulas are also used to obtain jump conditions for the wave equation and other second order partial differential equations whose fields have finite discontinuities at an interface a similar application to second order vector identities yields a new set of jump identities these identities show that the normal and tangential components of the jump in a vector field are kinematically interdependent e g sh

hom stacks and restriction of scalars fix an algebraic space s and let x and y be separated artin stacks of finite presentation over s with finite diagonals over s we define a stack homs x y classifying morphisms between x and y assume that x is proper and flat over s and assume fppf locally on s that there exists a finite finitely presented flat cover z x with z an algebraic space then we show that homs x y is an artin stack with quasi compact and separated diagonal