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We have decided to discontinue the publication of preprints on our preprint server as of 1 March 2024. The publication culture within mathematics has changed so much due to the rise of repositories such as ArXiV (www.arxiv.org) that we are encouraging all institute members to make their preprints available there. An institute's repository in its previous form is, therefore, unnecessary. The preprints published to date will remain available here, but we will not add any new preprints here.

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