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arXiv · 1704.03352

Ulrich bundles on intersections of two 4-dimensional quadrics

Yonghwa Cho·Yeongrak Kim·Kyoung-Seog Lee
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Abstract

In this paper, we investigate the existence of Ulrich bundles on a smooth complete intersection of two $4$-dimensional quadrics in $\mathbb P^5$ by two completely different methods. First, we find good ACM curves and use Serre correspondence in order to construct Ulrich bundles, which is analogous to the construction on a cubic threefold by Casanellas-Hartshorne-Geiss-Schreyer. Next, we use Bondal-Orlov's semiorthogonal decomposition of the derived category of coherent sheaves to analyze Ulrich bundles. Using these methods, we prove that any smooth intersection of two 4-dimensional quadrics in $\mathbb P^5$ carries an Ulrich bundle of rank $r$ for every $r \ge 2$. Moreover, we provide a description of the moduli space of stable Ulrich bundles.

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Yonghwa Cho, Yeongrak Kim, Kyoung-Seog Lee. 2017-04-11. Ulrich bundles on intersections of two 4-dimensional quadrics. https://arxiv.org/abs/1704.03352

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