We work with irreducible projective varieties on an algebraically closed field of any characteristic, henceforth called varieties. The contents of this paper are: (1) a general criterion expressing the vanishing of the higher cohomology of a line bundle on a Cohen-Macaulay variety in terms of a certain first-order conditions on hyperplane sections. Such conditions involve gaussian maps and the ...

In this paper, we consider a finite, torsion-free module E over Gorenstein local ring. We provide sufficient conditions for to be of linear type and the Rees algebra R ( ) Cohen-Macaulay. Our results are obtained by constructing generic Bourbaki ideal I exploiting properties residual intersections .

We study reflexive modules over one dimensional Cohen-Macaulay rings. Our key technique exploits the concept of I I -Ulrich modules.

In a previous article (J. Algebra 367 (2012), 142-165) we established axiomatic parametrised Cohen-Macaulay approximation which in particular was applied to pairs consisting of finite type flat family rings and modules. this sequel study the induced maps deformation functors deduce properties like smoothness injectivity under general, mainly cohomological conditions on module.

In the winter of 1999 I gave a series of lectures at Queen’s university about some recent results concerning the Cohen-Macaulay property of invariants of Hopf algebras. Tony Geramita asked me to write up my notes for the Queen’s Papers, and I happily took up his suggestion. Although this article focuses on the proof of one main theorem (Theorem 2.11 on page 12), it has some of the character of ...

We study the coordinate ring of an $L$-convex polyomino, determine its regularity in terms maximal number rooks that can be placed polyomino. also characterize Gorenstein polyominoes and those which are on punctured spectrum, compute Cohen–Macaulay type any polyomino rectangles covering it. Though main results algebraic nature, all proofs combinatorial.

Abstract We investigate the arrangement of hypersurfaces on a nonsingular varieties whose associated logarithmic vector bundle is arithmetically Cohen–Macaulay (for short, aCM), and prove that projective space only smooth complete intersection with Picard rank one admits an aCM bundle. also obtain number results bundles over several specific varieties. As opposite situation we Torelli‐type prob...

A tetrahedral curve is a (usually nonreduced) curve in P defined by an unmixed, height two ideal generated by monomials. We characterize when these curves are arithmetically Cohen-Macaulay by associating a graph to each curve and, using results from combinatorial commutative algebra and Alexander duality, relating the structure of the complementary graph to the Cohen-Macaulay property.