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Representation stability for syzygies of line bundles on Segre–Veronese varieties

Claudiu Raicu (2016)

Journal of the European Mathematical Society

The rational homology groups of packing complexes are important in algebraic geometry since they control the syzygies of line bundles on projective embeddings of products of projective spaces (Segre–Veronese varieties). These complexes are a common generalization of the multidimensional chessboard complexes and of the matching complexes of complete uniform hypergraphs, whose study has been a topic of interest in combinatorial topology. We prove that the multivariate version of representation stability,...

Résolution des fibrés généraux stables de rang 2 sur 3 de classes de Chern c 1 = - 1 , c 2 = 2 p 6  : I

Olivier Rahavandrainy (2010)

Annales de la faculté des sciences de Toulouse Mathématiques

On considère l’espace de modules M ( c 1 , c 2 ) des fibrés stables de rang 2 sur k 3 , de classes de Chern c 1 , c 2 , k étant un corps algébriquement clos de caractéristique quelconque. Si ( c 1 = 0 , c 2 > 0 ) ou ( c 1 = - 1 , c 2 = 2 p 6 ), on sait ([7], [9]) que M ( c 1 , c 2 ) a une composante irréductible dont le point générique ( c 1 , c 2 ) a la cohomologie naturelle. Nous avons calculé ([16]) la résolution minimale de ( 0 , c 2 ) . Dans cet article, nous voulons déterminer celle de ( - 1 , c 2 ) si c 2 > ( v + 2 ) ( 2 v 2 + 3 v - 1 ) 6 v + 7 , v est le plus petit entier tel que h 0 ( ( v ) ) > 0 . Par un procédé standard rappelé dans [16], on se ramène à des...

Restricted homological dimensions over local homomorphisms and Cohen-Macaulayness

Fangdi Kong, Dejun Wu (2018)

Czechoslovak Mathematical Journal

We define and study restricted projective, injective and flat dimensions over local homomorphisms. Some known results are generalized. As applications, we show that (almost) Cohen-Macaulay rings can be characterized by restricted homological dimensions over local homomorphisms.

Rings with divisibility on descending chains of ideals

Oussama Aymane Es Safi, Najib Mahdou, Ünsal Tekir (2024)

Czechoslovak Mathematical Journal

This paper deals with the rings which satisfy D C C d condition. This notion has been introduced recently by R. Dastanpour and A. Ghorbani (2017) as a generalization of Artnian rings. It is of interest to investigate more deeply this class of rings. This study focuses on commutative case. In this vein, we present this work in which we examine the transfer of these rings to the trivial, amalgamation and polynomial ring extensions. We also investigate the relationship between this class of rings and the...

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