We describe some recent work concerning Gorenstein liaison of codimension two subschemes of a projective variety. Applications make use of the algebraic theory of maximal Cohen–Macaulay modules, which we review in an Appendix.

In this paper, from an arbitrary smooth projective curve of genus at least two, we construct a non-Gorenstein Cohen-Macaulay normal domain and a nonfree totally reflexive module over it.

For real projective spaces, (a) the Euclidean immersion dimension, (b) the existence of axial maps, and (c) the topological complexity are known to be three facets of the same problem. This paper describes the corresponding relationship between the symmetrized versions of (b) and (c) to the Euclidean embedding dimension of projective spaces. Extensions to the case of 2e torsion lens spaces and ...

For an affine, toric I Q-Gorenstein variety Y (given by a lattice polytope Q) the vector space T 1 of infinitesimal deformations is related to the complexified vector spaces of rational Minkowski summands of faces of Q. Moreover, assuming Y to be an isolated, at least 3-dimensional singularity, Y will be rigid unless it is even Gorenstein and dimY = 3 (dimQ = 2). For this particular case, so-ca...

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...

Let Λ and Γ be artin algebras and ΛUΓ a faithfully balanced selforthogonal bimodule. In this paper, we first introduce the notion of k-Gorenstein modules with respect to ΛUΓ and then establish the left-right symmetry of the notion of k-Gorenstein modules, which develops a classical result of Auslander. As an application, we study the properties of dual modules relative to Gorenstein bimodules. ...

Abstract We show that finitely generated Cox rings are Gorenstein. This leads to a refined characterization of varieties Fano type: they exactly those projective with Gorenstein canonical quasicone ring. then for type and Kawamata log terminal quasicones X , iteration is finite factorial master In particular, even if the class group has torsion, we can express such as quotients by solvable redu...

We prove that every projective embedding of a connected scheme determined by the complete linear series of a sufficiently ample line bundle is defined by the 2×2 minors of a 1-generic matrix of linear forms. Extending the work of Eisenbud-Koh-Stillman for integral curves, we also provide effective descriptions for such determinantally presented ample line bundles on products of projective space...

In this paper we describe the facets cone associated to transversal polymatroid presented by A = {{1, 2}, {2, 3}, . . . , {n − 1, n}, {n, 1}}. Using the Danilov-Stanley theorem to characterize the canonicale module, we deduce that the base ring associated to this polymatroid is Gorenstein ring. Also, starting from this polymatroid we describe the transversal polymatroids with Gorenstein base ri...