embeddings into k efficient groups abstract we prove a theorem with the following corollary for each integer k 1 an arbitrary finite group g embeds into some finite group gk for which there exists an eilenberg mac lane cw space x k gk 1 whose finite n skeleton xn has euler poincare characteristic xn 1 1 ndhn gk for all n k the theorem can be viewed as a generalisation of a result of j harlander 1996 j algebra182 511 521 on the embedding of finite groups into groups with efficient presentations

characterization of log del pezzo pairs via anticanonical models we give a characterization of log del pezzo pairs in terms of their anticanonical models as a first application we show that every non rational del pezzo surface with log canonical singularities is of picard number one and contains a unique singularity which is simple elliptic as a second application we verify a conjecture of smith and schwede in dimension two which says that every surface of globally f regular type is of fano type

deficiency zero presentations for certain perfect groups in this paper we give two generator two relation presentations for the following perfect groups which were not previously known to have deficiency zero sl 2 32 sl 2 64 sl 2 27 sl 2 49 7 z 8 sl 2 5 sl 2 5 sl 2 5 sl 2 25 we also give two generator two relation presentations for three other finite perfect groups two having sl 2 7 as an image and one having sl 2 5 as an image we also discuss presentations for certain other perfect groups which were known to have deficiency zero and find some neat new presentations for them

high order differentiation filters that work reliable derivatives of digital images have always been hard to obtain especially but not only at high orders we analyze the sources of errors in traditional filters such as derivatives of the gaussian that are used for differentiation we then study a class of filters which is much more suitable for our purpose namely filters that preserve polynomials up to a given order we show that the errors in differentiation can be corrected using these filters we derive a condition for the validity domain of these filters involving some characteristics of the filter and of the shape our experiments show a very good performance for smooth functions

on images of weak fano manifolds we consider a smooth projective morphism between smooth complex projective varieties if the source space is a weak fano or fano manifold then so is the target space our proof is hodge theoretic we do not need mod p reduction arguments we also discuss related topics and questions

globally f regular and log fano varieties abstract we prove that every globally f regular variety is log fano in other words if a prime characteristic variety x is globally f regular then it admits an effective q divisor such that k x is ample and x has controlled kawamata log terminal in fact globally f regular singularities a weak form of this result can be viewed as a prime characteristic analog of de fernex and hacon s new point of view on kawamata log terminal singularities in the non q gorenstein case we also prove a converse statement in characteristic zero every log fano variety has globally f regular type our techniques apply also to f split varieties which we show to satisfy a log calabi yau condition we also prove a kawamata viehweg vanishing theorem for globally f regular pairs

remarks on proficient groups if a finite group g has a presentation with d generators and r relations it is well known that r d is at least the rank of the schur multiplier of g a presentation is called efficient if equality holds there is an analogous definition for proficient profinite presentations we show that many perfect groups have proficient presentations moreover we prove that infinitely many alternating groups symmetric groups and their double covers have proficient presentations

pro finite presentations the goal of this paper is to start to present a systematic presentation theory for pro finite groups let g be a fixed finitely generated pro finite group and p a free presentation of it i e p 1 r f g 1 is an exact sequence when f is a finitely generated free pro finite group we write d f for the minimal number of generators of f and d r for f the minimal number of generators of r as a normal subgroup of f in g2 gruenberg presented a systematic study of presentation theory of a discrete group g mainly for a finite group g and presented three basic problems question 1 given p 1 r f g 1 for i 1 2 when f is i i a free group is then d r d r f 1 f 2

rees algebras of f regular type abstract we study the f regularity of rees algebras r i a it in terms of the global f regularity of the blowing up x proj r i of spec a as it reads global f regularity is a global analog of strong f regularity defined via splitting of frobenius maps in prime characteristic and these notions are extended to characteristic zero by reduction modulo p 0 we study in detail the case where a m is a two dimensional local ring and i is an m primary ideal in characteristic zero the condition for r i to have f regular type is described in terms of the dual graph of a resolution x on which i o x is invertible we also prove some miscellaneous results concerning singularities of rees algebras and extended rees algebras of higher dimension

closing the relation gap by direct product stabilization abstract the generation gap of a group g is the difference between the minimal number of generators of g and the rank of the augmentation ideal the relation gap of a presentation f n is the difference between the minimal number of elements that generate n as a normal subgroup and the minimal number of g module generators of the relation module n n n we show that if g is a finitely presented group then there exists n such that g i 1 n z p z p being the cyclic group of order p has zero generation and zero relation gap we apply this result to questions concerning the efficiency of finite groups

curvature of vector bundles associated to holomorphic fibrations let l be a semi positive line bundle over a kahler manifold x fibered over a complex manifold y assuming the fibers are compact and nonsingular we prove that the hermitian vector bundle e over y whose fibers over points y are the spaces of global sections over xy to l kx y endowed with the l2 metric is semi positive in the sense of nakano we also discuss various applications among them a partial result on a conjecture of griffiths on the positivity of ample bundles

subadjunction of log canonical divisors ii we extend a subadjunction formula of log canonical divisors as in kawamata contemp math 207 1997 79 88 to the case when the codimension of the minimal center is arbitrary by using the positivity of the hodge bundles

presentations of finite simple groups a quantitative approach there is a constant such that all nonabelian finite simple groups of rank over with the possible exception of the ree groups have presentations with at most generators and relations and total length at most as a corollary we deduce a conjecture of holt there is a constant such that for every finite simple group every prime and every irreducible module