A compressed polytope is an integral convex polytope all of whose pulling triangulations are unimodular. A (q − 1)-simplex Σ each of whose vertices is a vertex of a convex polytope P is said to be a special simplex in P if each facet of P contains exactly q − 1 of the vertices of Σ. It will be proved that there is a special simplex in a compressed polytope P if (and only if) its toric ring K[P]...

We give geometric constructions of families of graded Gorenstein Artin algebras, some of which span a component of the space Gor(T ) parametrizing Gorenstein Artin algebras with a given Hilbert function T . This gives a lot of examples where Gor(T ) is reducible. We also show that the Hilbert function of a codimension four Gorenstein Artin algebra can have an arbitrarily long constant part with...

A finite p-group is said to be of Gorenstein-Kulkarni type if the set of all elements of non-maximal order is a maximal subgroup. 2-groups of Gorenstein-Kulkarni type arise naturally in the study of group actions on compact Riemann surfaces. In this paper, we proceed towards a classification of p-groups of Gorenstein-Kulkarni type. Mathematics Subject Classification: 20D15, 20E15, 30F20.

A main ingredient for Kustin–Miller unprojection, as developed in [PR], is the module HomR(I, ωR), where R is a local Gorenstein ring and I a codimension one ideal with R/I Gorenstein. We prove a method of calculating it in a relative setting using resolutions. We give three applications. In the first we generalise a result of [CFHR]. The second and the third are about Tom and Jerry, two famili...

In this paper, we study a particular case of Gorenstein projective, injective, and flat modules, which we call, respectively, strongly Gorenstein projective, injective, and flat modules. These last three classes of modules give us a new characterization of the first modules, and confirm that there is an analogy between the notion of “Gorenstein projective, injective, and flat modules”and the no...

Max Noether’s Theorem asserts that if ω is the dualizing sheaf of a nonsingular nonhyperelliptic projective curve then the natural morphisms SymH(ω) → H(ω) are surjective for all n ≥ 1. This is true for Gorenstein nonhyperelliptic curves as well. We prove this remains true for nearly Gorenstein curves and for all integral nonhyperelliptic curves whose non-Gorenstein points are unibranch. The re...

We examine some recent work of Phillip Griffith on étale covers and fibered products from the point of view of tight closure theory. While it is known that cyclic covers of Gorenstein rings with rational singularities are Cohen-Macaulay, we show this is not true in general in the absence of the Gorenstein hypothesis. Specifically, we show that the canonical cover of a Q-Gorenstein ring with rat...

In this article, we describe explicitely the Gorenstein locus of all minuscule Schubert varieties. This proves a special case of a conjecture of A. Woo and A. Yong [WY06b] on the Gorenstein locus of Schubert varieties.

Firstly, we see that the bases of miniversal deformations isolated Q \mathbb {Q} </mml:semant...

Gorenstein homological dimensions are refinements of the classical homological dimensions, and finiteness singles out modules with amenable properties reflecting those of modules over Gorenstein rings. As opposed to their classical counterparts, these dimensions rarely come with practical and robust criteria for finiteness, even over commutative noetherian local rings. Indeed, over such a ring ...