Ulrich subvarieties and the non-existence of low rank Ulrich bundles on complete intersections

Angelo Felice Lopez; Debaditya Raychaudhury

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arXiv · 2405.01154

Ulrich subvarieties and the non-existence of low rank Ulrich bundles on complete intersections

Angelo Felice Lopez·Debaditya Raychaudhury

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Abstract

We characterize the existence of an Ulrich vector bundle on a variety $X \subset P^N$ in terms of the existence of a subvariety satisfying some precise conditions. Then we use this fact to prove that a complete intersection of dimension $n \ge 4$, which if $n=4$ is very general and not of type $(2,2)$, does not carry any Ulrich bundles of rank $r \le 3$ unless $n=4, r=2$ and $X$ is a quadric.

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Angelo Felice Lopez, Debaditya Raychaudhury. 2024-05-02. Ulrich subvarieties and the non-existence of low rank Ulrich bundles on complete intersections. https://arxiv.org/abs/2405.01154

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