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arXiv · 2011.12622

Ulrich bundles on cubic fourfolds

Daniele Faenzi·Yeongrak Kim
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Abstract

We show the existence of rank 6 Ulrich bundles on a smooth cubic fourfold. First, we construct a simple sheaf E of rank 6 as an elementary modification of an ACM bundle of rank 6 on a smooth cubic fourfold. Such an E appears as an extension of two Lehn-Lehn-Sorger-van Straten sheaves. Then we prove that a general deformation of E(1) becomes Ulrich. In particular, this says that general cubic fourfolds have Ulrich complexity 6.

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Daniele Faenzi, Yeongrak Kim. 2020-11-25. Ulrich bundles on cubic fourfolds. https://arxiv.org/abs/2011.12622

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