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This article is cited in 2 scientific papers (total in 2 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
$H^2=2rs$, $r,s\ge1$. 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 $\rho(X)=\operatorname{rk}N(X)\le2$
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.
DOI:
https://doi.org/10.4213/im1130
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English version:
Izvestiya: Mathematics, 2008, 72:3, 497–508
Bibliographic databases:
UDC:
512.774+512.723
MSC: 14J28, 14J60 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
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http://mi.mathnet.ru/eng/izv1130https://doi.org/10.4213/im1130 http://mi.mathnet.ru/eng/izv/v72/i3/p89
Citing articles on Google Scholar:
Russian citations,
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Related articles on Google Scholar:
Russian articles,
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This publication is cited in the following articles:
-
Viacheslav V. Nikulin, “Self-correspondences of K3 surfaces via moduli of sheaves and arithmetic hyperbolic reflection groups”, Proc. Steklov Inst. Math., 273 (2011), 229–237
-
Madonna C.G., “On some moduli spaces of bundles on $K3$ surfaces, II”, Proc. Amer. Math. Soc., 140:10 (2012), 3397–3408
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