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Self-correspondences of K3 surfaces via moduli of sheaves and arithmetic hyperbolic reflection groups

  • Viacheslav V. Nikulin
Article

Abstract

In a series of our papers with Carlo Madonna (2002–2008), we described self-correspondences of a K3 surface over ℂ via moduli of sheaves with primitive isotropic Mukai vectors for the Picard number 1 or 2 of the K3 surfaces. Here we give a natural and functorial answer to the same problem for an arbitrary Picard number. As an application, we characterize, in terms of self-correspondences via moduli of sheaves, K3 surfaces with reflective Picard lattice, that is, when the automorphism group of the lattice is generated by reflections up to finite index. It is known since 1981 that the number of reflective hyperbolic lattices is finite. We also formulate some natural unsolved related problems.

Keywords

Modulus Space Vector Bundle Automorphism Group STEKLOV Institute Integral Action 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Pleiades Publishing, Ltd. 2011

Authors and Affiliations

  1. 1.Department of Pure MathematicsUniversity of LiverpoolLiverpoolUK
  2. 2.Steklov Mathematical InstituteRussian Academy of SciencesMoscowRussia

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