Verlinde bundles of families of hypersurfaces and their jumping lines

Orlando Marigliano

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arXiv · 1804.05710

Verlinde bundles of families of hypersurfaces and their jumping lines

Orlando Marigliano

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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 $\mathbb P^n$ and calculate the cohomology class of the locus of jumping lines of the Verlinde bundles $V_{d+1}$ in the cases $n=2,3$.

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Orlando Marigliano. 2018-04-16. Verlinde bundles of families of hypersurfaces and their jumping lines. https://arxiv.org/abs/1804.05710

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