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arXiv · 2008.07313

On the positivity of the first Chern class of an Ulrich vector bundle

Angelo Felice Lopez
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Abstract

We study the positivity of the first Chern class of a rank r Ulrich vector bundle E on a smooth n-dimensional variety $X \subseteq \mathbb P^N$. We prove that $c_1(E)$ is very positive on every subvariety not contained in the union of lines in X. In particular if X is not covered by lines, then E is big and $c_1(E)^n \ge r^n$. Moreover we classify rank r Ulrich vector bundles E with $c_1(E)^2=0$ on surfaces and with $c_1(E)^2=0$ or $c_1(E)^3=0$ on threefolds (with some exceptions).

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Angelo Felice Lopez. 2020-08-17. On the positivity of the first Chern class of an Ulrich vector bundle. https://doi.org/10.1142/s0219199721500711

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