On Codimension Two Subvarieties in Hypersurfaces

Multiplicities of Simple Closed Geodesics and Hypersurfaces in Teichmüller Space

Using geodesic length functions, we define a natural family of real codimension 1 subvarieties of Teichmüller space, namely the subsets where the lengths of two distinct simple closed geodesics are of equal length. We investigate the point set topology of the union of all such hypersurfaces using elementary methods. Finally, this analysis is applied to investigate the nature of the Markoff conj...

Lifting Problem in Codimension 2 and Initial Ideals

On subcanonical Gorenstein varieties and apolarity

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.

On a Special Class of Smooth Codimension Two Subvarieties

We work on an algebraically closed field of characteristic zero. By Lefschetz’s theorem, a smooth codimension two subvariety X ⊂ P, n ≥ 4, which is not a complete intersection, lying on a hypersurface Σ, verifies dim(X ∩ Sing(Σ)) ≥ n− 4. In this paper we deal with a situation in which the singular locus of Σ is as large as can be, but, at the same time, the simplest possible: we assume Σ is an ...

Subcanonicity of Codimension Two Subvarieties

We prove that smooth subvarieties of codimension two in Grassmannians of lines of dimension at least six are rationally numerically subcanonical. We prove the same result for smooth quadrics of dimension at least six under some extra condition. The method is quite easy, and only uses Serre’s construction, Porteous formula and Hodge index theorem.