The stringy E-function for normal irreducible complex varieties with at worst log terminal singularities was introduced by Batyrev. It is defined by data from a log resolution. If the variety is projective and Gorenstein and the stringy E-function is a polynomial, Batyrev also defined the stringy Hodge numbers as a generalization of the Hodge numbers of nonsingular projective varieties, and con...

Batyrev has defined the stringy E-function for complex varieties with at most log terminal singularities. It is a rational function in two variables if the singularities are Gorenstein. Furthermore, if the variety is projective and its stringy E-function is a polynomial, Batyrev defined its stringy Hodge numbers essentially as the coefficients of this E-function, generalizing the usual notion o...

In this paper, we establish, as a generalization of a result on the classical homological dimensions of commutative rings, an upper bound on the Gorenstein global dimension of commutative rings using the global cotorsion dimension of rings. We use this result to compute the Gorenstein global dimension of some particular cases of trivial extensions of rings and of group rings.

Fix integers r, k, g with r > k > 0 and g ≥ 2. Let X be an integral projective curve with g := pa(X) and E a rank r torsion free sheaf on X which is a flat limit of a family of locally free sheaves on X. Here we prove the existence of a rank k subsheaf A of E such that r(deg(A)) ≥ k(deg(E)) − k(r − k)g. We show that for every g ≥ 9 there is an integral projective curve X,X not Gorenstein, and a...

We characterize the cd-indices of Gorenstein* posets of rank 5, equivalently the flag f -vectors of Gorenstein* order complexes of dimension 3. As a corollary, we characterize the f -vectors of Gorenstein* order complexes in dimensions 3 and 4. This characterization rise a speculated intimate connection between the f -vectors of flag homology spheres and the f -vectors of Gorenstein* order comp...

Let X be a projective minimal Gorenstein 3-fold of general type with canonical singularities. We prove that the 5canonical map is birational onto its image.

In this paper, we classify projective toric birational morphisms from Gorenstein toric 3-folds onto the 3-dimensional affine space with relatively ample anti-canonical divisors.

We characterize the cd-indices of Gorenstein* posets of rank 5, equivalently the flag f -vectors of Gorenstein* order complexes of dimension 3. As a corollary, we characterize the f -vectors of Gorenstein* order complexes in dimensions 3 and 4. This characterization rise a speculated intimate connection between the f -vectors of flag homology spheres and the f -vectors of Gorenstein* order comp...