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Trudy Matematicheskogo Instituta imeni V.A. Steklova, 2011, Volume 273, Pages 247–256
(Mi tm3279)
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This article is cited in 1 scientific paper (total in 1 paper)
Self-correspondences of K3 surfaces via moduli of sheaves and arithmetic hyperbolic reflection groups
Viacheslav V. Nikulinab a Steklov Mathematical Institute, Russian Academy of Sciences, Moscow, Russia
b Department of Pure Mathematics, University of Liverpool, Liverpool, UK
Abstract:
In a series of our papers with Carlo Madonna (2002–2008), we described self-correspondences of a K3 surface over $\mathbb C$ 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.
Received in December 2009
Citation:
Viacheslav V. Nikulin, “Self-correspondences of K3 surfaces via moduli of sheaves and arithmetic hyperbolic reflection groups”, Modern problems of mathematics, Collected papers. In honor of the 75th anniversary of the Institute, Trudy Mat. Inst. Steklova, 273, MAIK Nauka/Interperiodica, Moscow, 2011, 247–256; Proc. Steklov Inst. Math., 273 (2011), 229–237
Linking options:
https://www.mathnet.ru/eng/tm3279 https://www.mathnet.ru/eng/tm/v273/p247
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