negative holomorphic curvature and positive canonical bundle in this note we show that if a projective manifold admits a kahler metric with negative holomorphic sectional curvature then the canonical bundle of the manifold is ample this confirms a conjecture of the second author

an extension of a theorem of wu yau we show that a compact kahler manifold with nonpositive holomorphic sectional curvature has nef canonical bundle if the holomorphic sectional curvature is negative then it follows that the canonical bundle is ample confirming a conjecture of yau the key ingredient is the recent solution of this conjecture in the projective case by wu yau

hermitian metrics of positive holomorphic sectional curvature on fibrations the main result of this note essentially is that if the base and fibers of a compact fibration carry hermitian metrics of positive holomorphic sectional curvature then so does the total space of the fibration the proof is based on the use of a warped product metric as in the work by cheung in case of negative holomorphic sectional curvature but differs in certain key aspects e g in that it does not use the subadditivity property for holomorphic sectional curvature due to grauert reckziegel and wu

the multiple holomorph of a finitely generated abelian group w h mills has determined for a finitely generated abelian group g the regular subgroups n gn g of s g s g the group of permutations on the set g which have the same holomorph as g that is such that ns g n ns g g ns g n ns g g where is the right regular representation we give an alternative approach to mills result which relies on a characterization of the regular subgroups of ns g g ns g g in terms of commutative ring structures on g we are led to solve for the case of a finitely generated abelian group g the following problem given an abelian group g g what are the commutative ring structures g g such that all automorphisms of g as a group are also automorphisms of g as a ring

bi skew braces and regular subgroups of the holomorph abstract l childs has defined a skew brace g to be a bi skew brace if g is also a skew brace and has given applications of this concept to the equivalent theory of hopf galois structures the goal of this paper is to deal with bi skew braces g from the yet equivalent point of view of regular subgroups of the holomorph of g in particular we find that certain groups studied by t kohl f dalla volta and the author and c tsang all yield examples of bi skew braces building on a construction of childs we also give various methods for exhibiting further examples of bi skew braces

solutions of the yang baxter equation associated with a left brace abstract given a left brace b a method is given to construct explicitly all the non degenerate involutive set theoretic solutions x r of the yang baxter equation such that the associated permutation group g x r is isomorphic as a left brace to b this method depends entirely on the brace structure of b

hermitian metrics of negative holomorphic sectional curvature on some hyperbolic manifolds on montre que pour certains types de varietes hyperboliques compactes on peut construire une metrique hermitienne dessus avec partout une courbure sectionnelle holomorphe negative

analysis and numerical simulation of positive and dead core solutions of singular two point boundary value problems we investigate the solvability of the dirichlet boundary value problem u t lg u t l 0 u 0 1 u 1 1 where l is a nonnegative parameter we discuss the existence of multiple positive solutions and show that for certain values of l there also exist solutions that vanish on a subinterval r 1 r 0 1 the so called dead core solutions in order to illustrate the theoretical findings we present computational results for g u 1 u computed using the collocation method implemented in bvpsuite a new version of the standard matlab code sbvp1 0

groups that have the same holomorph as a finite perfect group abstract we describe the groups that have the same holomorph as a finite perfect group our results are complete for centerless groups when the center is non trivial some questions remain open the peculiarities of the general case are illustrated by a couple of examples that might be of independent interest

hopf galois structures on extensions of degree p2q and skew braces of order p2q the cyclic sylow p subgroup case abstract let p q be distinct primes with p 2 we classify the hopf galois structures on galois extensions of degree p 2 q such that the sylow p subgroups of the galois group are cyclic this we do according to greither and pareigis and byott by classifying the regular subgroups of the holomorphs of the groups g of order p 2 q in the case when the sylow p subgroups of g are cyclic this is equivalent to classifying the skew braces g furthermore we prove that if g and are groups of order p 2 q with non isomorphic sylow p subgroups then there are no regular subgroups of the holomorph of g which are isomorphic to equivalently a galois extension with galois group has no hopf galois structures of type g our method relies on the alternate brace operation on g which we use mainly indirectly that is in terms of the functions g aut g defined by g x x g g 1 these functions are in one to one correspondence with the regular subgroups of the holomorph of g and are characterised by the functional equation g h h g h for g h g we develop methods to deal with these functions with the aim of making their enumeration easier and more conceptual

families of rationally connected varieties recall that a proper variety x is said to be rationally connected if two general points p q x are contained in the image of a map g p x this is clearly a birationally invariant property when x is smooth this turns out to be equivalent to the a priori weaker condition that two general points can be joined by a chain of rational curves and also to the a priori stronger condition that for any finite subset x there is a map g p x whose image contains and such that gtx is an ample bundle

reduction of manifolds with semi negative holomorphic sectional curvature in this note we continue the investigation of a projective kahler manifold m of semi negative holomorphic sectional curvature h we introduce a new differential geometric numerical rank invariant which measures the number of linearly independent truly flat directions of h in the tangent spaces we prove that this invariant is bounded above by the nef dimension and bounded below by the numerical kodaira dimension of m we also prove a splitting theorem for m in terms of the nef dimension and under some additional hypotheses in terms of the new rank invariant

on the multiple holomorph of groups of squarefree or odd prime power order abstract let g be a group and write perm g for its symmetric group let us define hol g to be the holomorph of g regarded as a subgroup of perm g and let nhol g denote its normalizer the quotient t g nhol g hol g has been computed for various families of groups g and in most of the known cases it turns out to be elementary 2 abelian except for two groups of order 16 and some groups of odd prime power order and nilpotency class two in this paper we shall show that t g is elementary 2 abelian for all finite groups g of squarefree order and that t g is not a 2 group for certain finite p groups g of nilpotency class at most p 1

multiple holomorphs of finite p groups of class two abstract let g be a group and s g be the group of permutations on the set g the abstract holomorph of g is the natural semidirect product aut g g we will write hol g for the normalizer of the image in s g of the right regular representation of g hol g n s g g aut g g aut g g and also refer to it as the holomorph of g more generally if n is any regular subgroup of s g then n s g n is isomorphic to the holomorph of n g a miller has shown that the group t g n s g hol g hol g acts regularly on the set of the regular subgroups n of s g which are isomorphic to g and have the same holomorph as g in the sense that n s g n hol g if g is non abelian inversion on g yields an involution in t g other non abelian regular subgroups n of s g having the same holomorph as g yield other involutions in t g in the cases studied in the literature t g turns out to be a finite 2 group which is often elementary abelian in this paper we exhibit an example of a finite p group g p of class 2 for p 2 a prime which is the smallest p group such that t g p is non abelian and not a 2 group moreover t g p is not generated by involutions when p 3 more generally we develop some aspects of a theory of t g for g a finite p group of class 2 for p 2 in particular we show that for such a group g there is an element of order p 1 in t g and exhibit examples where t g p 1 and others where t g contains a large elementary abelian p subgroup

singular langmuir hinshelwood reaction diffusion problems strong adsorption under quasi isothermal conditions we consider the steady state reaction diffusion problem for a permeable catalytic particle with langmuir hinshelwood kinetics under isothermal and quasi isothermal conditions it is known that there may be multiple solutions due to either strong adsorption or external thermal effects in the first case an arbitrarily large number of solutions may appear for symmetric pellets in two and three dimensions an asymptotic analysis provides analytical expressions for the response curve of the particle and for the multiplicity bounds the approximate results compare quite well with those computed numerically even in cases in which the gauge functions of the approximation scheme are of the logarithmic type