Fabrizio Anella ; Andreas Höring - The cotangent bundle of K3 surfaces of degree two

epiga:9960 - Épijournal de Géométrie Algébrique, July 10, 2023, Special volume in honour of Claire Voisin - https://doi.org/10.46298/epiga.2023.9960
The cotangent bundle of K3 surfaces of degree twoArticle

Authors: Fabrizio Anella ; Andreas Höring

    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 $D_S \subset \mathbb{P}(\Omega_S)$ that plays a similar role to the surface of bitangents for a quartic in $\mathbb{P}^3$.

    Comment: 30 pages

    https://doi.org/10.46298/epiga.2023.9960
    Source: arXiv.org:2207.09294
    Volume: Special volume in honour of Claire Voisin
    Published on: July 10, 2023
    Accepted on: March 27, 2023
    Submitted on: August 24, 2022
    Keywords: Mathematics - Algebraic Geometry
    Licence: Attribution-ShareAlike 4.0 International (CC BY-SA 4.0)
    Funding:
      Source : OpenAIRE Graph
    • Modern Aspects of Geometry: Categories, Cycles and Cohomology of Hyperkähler Varieties; Funder: European Commission; Code: 854361
    • Foliations and algebraic geometry; Funder: French National Research Agency (ANR); Code: ANR-16-CE40-0008

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