Ulrich bundles on intersections of two 4-dimensional quadrics
| Autor: | Yeongrak Kim, Kyoung-Seog Lee, Yonghwa Cho |
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| Rok vydání: | 2017 |
| Předmět: |
Derived category
Pure mathematics Rank (linear algebra) Mathematics::Commutative Algebra General Mathematics 010102 general mathematics 05 social sciences Complete intersection Algebraic geometry 01 natural sciences Moduli space Coherent sheaf Mathematics - Algebraic Geometry Mathematics::Algebraic Geometry Intersection Bundle 0502 economics and business FOS: Mathematics 0101 mathematics Algebraic Geometry (math.AG) 050203 business & management Mathematics |
| Zdroj: | International Mathematics Research Notices |
| DOI: | 10.48550/arxiv.1704.03352 |
| Popis: | 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. Comment: 25 pages |
| Databáze: | OpenAIRE |
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