Let X be a codimension 1 subvariety of dimension > 1 of a variety of minimal degree Y . If X is subcanonical with Gorenstein canonical singularities admitting a crepant resolution, then X is Arithmetically Gorenstein and we characterise such subvarieties X of Y via apolarity as those whose apolar hypersurfaces are Fermat.

We classify Fano 3-folds with canonical Gorenstein singularities whose anticanonical linear system has no base points but does not give an embedding, and we classify anticanonically embedded Fano 3-folds with canonical Gorenstein singularities which are not the intersection of quadrics.

In this paper we study the deformation and Q-Gorenstein deformation theory of schemes with non-isolated singularities. We obtain obstruction spaces for the existence of deformations and also for local deformations to exist globally. Finally we obtain explicit criteria in order for a pure and reduced scheme of finite type over a field k to have smoothings and Q-Gorenstein smoothings.

Datatypes which differ inessentially in their names and structure are said to be isomorphic; for example, a ternary product is isomorphic to a nested pair of binary products. In some canonical cases, the conversion function is uniquely determined solely by the two types involved. In this article we describe and implement a program in Generic Haskell which automatically infers this function by n...

Abstract Matroid base polytope and independence are Cohen–Macaulay. There plenty of examples when they also Gorenstein. We provide a full classification matroids whose or is This answers to question raised by Herzog Hibi.