We prove a vanishing theorem for the Hodge number h of projective toric varieties provided by a certain class of polytopes We explain how this Hodge number also gives information about the deformation theory of the toric Gorenstein singularity derived from the same polytope In particular the vanishing theorem for h implies that these deformations are unobstructed

Let X ⊂ P be a generically reduced projective scheme. A fundamental goal in computational algebraic geometry is to compute information about X even when defining equations for X are not known. We use numerical algebraic geometry to develop a test for deciding if X is arithmetically Gorenstein and apply it to three secant varieties.

We recall the basic geometric properties of the projective variety Latn r (K) parametrizing a family of special lattices over Witt vectors proved in [Hab05, HS, San04]. In this paper, we prove that a particular set of subvarieties of Latn r (K) are normal and Gorenstein. The set contains the subregular variety, that is, the complement of the smooth locus, of Latn r (K).

The so-called ’change-of-ring’ results are well-known expressions which present several connections between projective, injective and flat dimensions over the various base rings. In this note we extend these results to the Gorenstein dimensions over Cohen-Macaulay local rings.

We prove a vanishing theorem for the Hodge number h 2;1 of projective toric varieties provided by a certain class of polytopes. We explain how this Hodge number also gives information about the deformation theory of the toric Gorenstein singularity derived from the same polytope. In particular, the vanishing theorem for h 2;1 implies that these deformations are unobstructed.

Let R be a commutative ring with identity and M an R–module. If M is either locally cyclic projective or faithful multiplication then M is locally either zero or isomorphic to R. We investigate locally cyclic projective modules and the properties they have in common with faithful multiplication modules. Our main tool is the trace ideal. We see that the module structure of a locally cyclic proje...

We show  that a projective maximal submodule of afinitely generated, regular, extending module is a directsummand. Hence, every finitely generated, regular, extendingmodule with projective maximal submodules is semisimple. As aconsequence, we observe that every regular, hereditary, extendingmodule is semisimple. This generalizes and simplifies a result of  Dung and   Smith. As another consequen...