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MiS Preprint
34/2018

Verlinde bundles of families of hypersurfaces and their jumping lines

Orlando Marigliano

Abstract

Verlinde bundles are vector bundles $V_k$ arising as the direct image $\pi_*(\mathcal L^{\otimes k})$ of polarizations of a proper family of schemes $\pi\colon \mathfrak X \to S$. 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 $|\mathcal{O}(d)|$ and calculate the cohomology class of the locus of jumping lines of the Verlinde bundles $V_{d+1}$ in the cases $n=2,3$.

Received:
May 2, 2018
Published:
Jun 18, 2018
Keywords:
Verlinde Bundles, Jumping Lines, Cohomology Class

Related publications

inJournal
2019 Journal Open Access
Orlando Marigliano

Verlinde bundles of families of hypersurfaces and their jumping lines

In: Beiträge zur Algebra und Geometrie, 60 (2019) 3, pp. 437-444