let $mathcal {a}$ be an abelian category with enough projective objects and $mathcal {x}$ be a full subcategory of $mathcal {a}$. we define gorenstein projective objects with respect to $mathcal {x}$ and $mathcal{y}_{mathcal{x}}$, respectively, where $mathcal{y}_{mathcal{x}}$=${ yin ch(mathcal {a})| y$ is acyclic and $z_{n}yinmathcal{x}}$. we point out that under certain hypotheses, these two g...

In this paper we construct Shimura subvarieties of dimension bigger than one the moduli space polarised abelian varieties a given dimension, which are generically contained in Pym loci (ramified) double covers. The idea is to adapt techniques already used curves Prym higher dimensional case, namely use families Galois covers projective line. case treated detail, since it possible make explicit ...

Let N be a bijective measure space. D. Sasaki’s classification of positive definite, globally universal domains was a milestone in homological Galois theory. We show that |O| ≤ K. The groundbreaking work of H. Thomas on contra-arithmetic planes was a major advance. Recent developments in analytic group theory [36, 36] have raised the question of whether Fréchet’s conjecture is false in the cont...

We prove that left cancellative right hereditary monoids satisfying the dedekind height property are precisely the Zappa-Szép products of free monoids and groups. The ‘fundamental’ monoids of this type are in bijective correspondence with faithful self-similar group actions. 2000 AMS Subject Classification: 20M10, 20M50. 1 A class of left cancellative monoids This paper develops some ideas that...

This paper is devoted to the study of products of classes of right $S$-posets possessing one of the flatness properties and preservation of such properties under products. Specifically, we characterize a pomonoid $S$ over which its nonempty products as right $S$-posets satisfy some known flatness properties. Generalizing this results, we investigate products of right $S$-posets satisfying Condi...

We obtain an explicit formula for the number of Lamé equations (modulo linear changes of variable) with index n and projective monodromy group of order 2N , for given n ∈ Z and N ∈ N. This is done by performing the combinatorics of the ‘dessins d’enfants’ associated to the Belyi covers which transform hypergeometric equations into Lamé equations by pull-back.

Let B be a smooth, connected, projective complex curve of genus h. For w ≥ 2d we prove the irreducibility of the Hurwitz stack H Sd (B) parametrizing degree d covers of B simply-branched over w points, and with monodromy group Sd.

We study properties of double covers of P ramified along nodal sextic surfaces such as non-rationality, Q-factoriality, potential density, and elliptic fibration structures. We also consider some relevant problems over fields of positive characteristic. 2000 Mathematics Subject Classification. Primary 14E05, 14E08, 14G05, 14G15, 14J17, 14J45. All varieties are assumed to be projective, normal, ...

We show that over an algebraically closed field of characteristic not equal to 2, homological projective duality for smooth quadric hypersurfaces and double covers spaces branched is a combination two operations: one interchanges hypersurface with its classical dual the other cover along it.

We study Galois covers of the projective line branched at three points with bad reduction to characteristic p, under the condition that p strictly divides the order of the Galois group. As an application of our results, we prove that the field of moduli of such a cover is at most tamely ramified at p.