We present sufficient conditions under which effective descent morphisms in a quasivariety of universal algebras are the same as regular epimorphisms and examples for which they are the same as regular epimorphisms satisfying projectivity. 1. Preliminaries A variety is a full subcategory of the category of structures for a first order (one sorted) language, closed under substructures, products ...

We describe examples motivated by the work of Serre and Abhyankar. Subject Class: Primary 11F22, 11F03. Secondary 30F35, 20C34.

RÉSUMÉ. Cet article étudie l’enveloppe réflective engendrée par une sous-catégorie pleine d’une catégorie complète. Il s’agit de la plus petite sous-catégorie qui est pleine et réflective. Comme application nous obtenons l’enveloppe coréflective de la sous-catégorie pleine de cubes pointés dans la catégorie des espaces topologiques pointés. Par la suite nous déterminons l’enveloppe réflective d...

Let k be a field and Q a finite quiver without oriented cycles. Let kQ be the path algebra of Q and mod kQ the category of k-finite-dimensional right kQ-modules. The cluster category CQ was introduced in [1] (for general Q) and, independently, in [4] (for Q of type An). It is defined as the orbit category of the bounded derived category D(mod kQ) under the action of the automorphism Σ−1 ◦ S, wh...

We begin a study of the intersection theory of the moduli spaces of degree two stable maps from two-pointed rational curves to arbitrary-dimensional projective space. First we compute the Betti numbers of these spaces using Serre polynomial and equivariant Serre polynomial methods developed by E. Getzler and R. Pandharipande. Then, via the excision sequence, we compute an additive basis for the...

We prove a general criterion which ensures that fractional Calabi--Yau category of dimension $\leq 2$ admits unique Serre-invariant stability condition, up to the action universal cover $\text{GL}^+_2(\mathbb{R})$. apply this result Kuznetsov component $\text{Ku}(X)$ cubic threefold $X$. In particular, we show all known conditions on are invariant with respect Serre functor and thus lie in same...

We give a characterization of non-hyperbolic pseudoconvex Reinhardt domains in C for which the answer to the Serre problem is positive.

We introduce sheaves and sheaf cohomology and use them to prove the Riemann-Roch theorem and Serre duality. The main proofs follow the treatment in Forster [3].