Verlinde bundles of families of hypersurfaces and their jumping lines

Abstract

Verlinde bundles are vector bundles $V_k$ arising as the direct image ${\pi }_{\ast }({\mathcal{L}}^{\otimes k})$ of polarizations of a proper family of schemes $\pi :\mathfrak{X}\to S$. We study the splitting behavior of Verlinde bundles in the case where $\pi$ is the universal family $\mathfrak{X}\to |\mathcal{O}(d)|$ of hypersurfaces of degree $d$ in ${\mathbb{P}}^n$ and calculate the cohomology class of the locus of jumping lines of the Verlinde bundles $V_{d+1}$ in the cases $n=2,3$.

arXiv commentThis version adds a missing definition in Prop. 2.2 and corrects minor typos