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This article is cited in 3 scientific papers (total in 3 papers)
Explicit correspondences of a K3 surface with itself
C. G. Madonnaa, V. V. Nikulinbc a Spanish National Research Council (Consejo Superior de Investigaciones Científicas)
b Steklov Mathematical Institute, Russian Academy of Sciences
c University of Liverpool
Abstract:
Let $X$ be a K3-surface with a polarization $H$ of degree $H^2=2rs$, $r,s\geqslant1$. We consider the moduli space $Y$ of sheaves over $X$ with a primitive isotropic Mukai vector $(r,H,s)$. This space is again a K3-surface. In earlier papers, we gave necessary and sufficient conditions (in terms of the Picard lattice $N(X)$) for $Y$ and $X$ to be isomorphic. Here we show that these conditions imply the existence of an isomorphism between $Y$ and $X$ which is a composite of certain universal geometric isomorphisms between moduli of sheaves over $X$ and Tyurin's geometric isomorphism between moduli of sheaves over $X$ and $X$ itself. It follows that a general K3-surface $X$ with $\rho(X)=\operatorname{rk}N(X)\leqslant2$ is isomorphic to $Y$ if and only if there is an isomorphism $Y\cong X$ which is a composite of universal isomorphisms and Tyurin's isomorphism.
Received: 10.07.2006
Citation:
C. G. Madonna, V. V. Nikulin, “Explicit correspondences of a K3 surface with itself”, Izv. RAN. Ser. Mat., 72:3 (2008), 89–102; Izv. Math., 72:3 (2008), 497–508
Linking options:
https://www.mathnet.ru/eng/im1130https://doi.org/10.1070/IM2008v072n03ABEH002409 https://www.mathnet.ru/eng/im/v72/i3/p89
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Abstract page: | 590 | Russian version PDF: | 184 | English version PDF: | 8 | References: | 51 | First page: | 11 |
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