1 citations · 1 across the 3 of their papers we have counts for
6 papers · 1 filter
Singularities of the Secant Variety
Pete Vermeire
We give positivity conditions on the embedding of a smooth variety which guarantee the normality of the secant variety, generalizing earlier results of the author and others. We al…
The Cohomology of Reflexive Sheaves on Smooth Projective 3-folds
Peter Vermeire
We study the cohomology of reflexive rank 2 sheaves on smooth projective threefolds. Applications are given to the moduli space of reflexive sheaves.
Moduli of Reflexive Sheaves on Smooth Projective 3-folds
Peter Vermeire
We compute the expected dimension of the moduli space of torsion-free rank 2 sheaves at a point corresponding to a stable reflexive sheaf and give conditions for the existence of a…
On the Regularity of Powers of Ideal Sheaves
Peter Vermeire
We use the geometry of the secant variety to an embedded smooth curve to prove some vanishing and regularity theorems for powers of ideal sheaves.
Secant Varieties and Birational Geometry
Peter Vermeire
We show how to use information about the equations defining secant varieties to smooth projective varieties in order to construct a natural collection of birational transformations…
Results on Secant Varieties Leading to a Geometric Flip Construction
Peter Vermeire
We study the relationship between the equations defining a projective variety and properties of its secant varieties. In particular, we use information about the syzygies among the…