Let ∆ ⊂ H be the germ of a non-normal surface along a proper curve with smooth components such that the high index points of H are semilog-terminal and the Gorenstein singular points are semi-log-canonical. We describe the sheaf T 1 qG(H) of Q-Gorenstein deformations of H, we show that T 1 qG(H)/(torsion) is a line bundle L on ∆ and we calculate the degree of the restriction of L on every irred...

A Gorenstein sequence H is a sequence of nonnegative integers H = (1, h1, . . . , hj = 1) symmetric about j/2 that occurs as the Hilbert function in degrees less or equal j of a standard graded Artinian Gorenstein algebra A = R/I , where R is a polynomial ring in r variables and I is a graded ideal. The scheme PGor(H) parametrizes all such Gorenstein algebra quotients of R having Hilbert functi...

Rings of invariants can have nice homological properties even if they do not have finite global dimension. Watanabe’s Theorem [W] gives conditions when the fixed subring of a commutative ring under the action of a finite group is a Gorenstein ring. The Gorenstein condition was extended to noncommutative rings by a condition explored by Idun Reiten in the 1970s, called k-Gorenstein in [FGR]. Thi...

Zaks (1969) proved that the answer is affirmative for a left and right noetherian ring if both dimensions are finite. Such rings are called Gorenstein. For a positive integer k, Auslander and Reiten (1994) initiated the study of k-Gorenstein algebras, which has stimulated several investigations. They showed that the answer to the question above is positive in case is an artin -Gorenstein algebr...

In this article we report on extensive calculations concerning the Gorenstein defect for Hecke algebras of spaces of modular forms of prime weight p at maximal ideals of residue characteristic p such that the attached mod p Galois representation is unramified at p and the Frobenius at p acts by scalars. The results lead us to the ask the question whether the Gorenstein defect and the multiplici...

This is a survey article on Gorenstein initial complexes of extensively studied ideals in commutative algebra and algebraic geometry. These include defining ideals of Segre and Veronese varieties, toric deformations of flag varieties known as Hibi ideals, determinantal ideals of generic matrices of indeterminates, and ideals generated by Pfaffians of generic skew symmetric matrices. We give a s...

Let (R,m, k) be a noetherian local ring. It is well-known that R is regular if and only if the injective dimension of k is finite. In this paper it is shown that R is Gorenstein if and only if the Gorenstein injective dimension of k is finite. On the other hand a generalized version of the so-called Bass formula is proved for finitely generated modules of finite Gorenstein injective dimension. ...