The cotangent bundle of K3 surfaces of degree two
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2022
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| _version_ | 1866916047515287552 |
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| author | Anella, Fabrizio Höring, Andreas |
| author_facet | Anella, Fabrizio Höring, Andreas |
| contents | K3 surfaces have been studied from many points of view, but the positivity of the cotangent bundle is not well understood. In this paper we explore the surprisingly rich geometry of the projectivised cotangent bundle of a very general polarised K3 surface $S$ of degree two. In particular, we describe the geometry of a surface $D_S \subset \mathbb{P}(Ω_S)$ that plays a similar role to the surface of bitangents for a quartic in $\mathbb{P}^3$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2207_09294 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | The cotangent bundle of K3 surfaces of degree two Anella, Fabrizio Höring, Andreas Algebraic Geometry K3 surfaces have been studied from many points of view, but the positivity of the cotangent bundle is not well understood. In this paper we explore the surprisingly rich geometry of the projectivised cotangent bundle of a very general polarised K3 surface $S$ of degree two. In particular, we describe the geometry of a surface $D_S \subset \mathbb{P}(Ω_S)$ that plays a similar role to the surface of bitangents for a quartic in $\mathbb{P}^3$. |
| title | The cotangent bundle of K3 surfaces of degree two |
| topic | Algebraic Geometry |
| url | https://arxiv.org/abs/2207.09294 |