4 papers
A noncombinatorial proof that toric rank 2 bundles on projective space split
David Stapleton
Hartshorne's conjecture about vector bundles on projective space states that any rank 2 vector bundle on n-dimensional projective space splits as soon as n is at least 7. Klyachko…
Maximal Chow constant and cohomologically constant fibrations
Kristin DeVleming, David Stapleton
Motivated by the study of rationally connected fibrations (and the MRC quotient) we study different notions of birationally simple fibrations. We say a fibration of smooth projecti…
The degree of irrationality of hypersurfaces in various Fano varieties
David Stapleton, Brooke Ullery
The purpose of this paper is to compute the degree of irrationality of hypersurfaces of sufficiently high degree in various Fano varieties: quadrics, Grassmannians, products of pro…
The tangent space of the punctual Hilbert scheme
Dori Bejleri, David Stapleton
The purpose of this paper is to study the Zariski tangent space of the punctual Hilbert scheme parametrizing subschemes of a smooth surface which are supported at a single point. W…