Open Access
January, 2012 Kummer's quartics and numerically reflective involutions of Enriques surfaces
Shigeru MUKAI
J. Math. Soc. Japan 64(1): 231-246 (January, 2012). DOI: 10.2969/jmsj/06410231


A (holomorphic) involution σ of an Enriques surface S is said to be numerically reflective if it acts on the cohomology group H2(S, Q) as a reflection. We show that the invariant sublattice H(S, σ; Z) of the anti-Enriques lattice H-(S, Z) under the action of σ is isomorphic to either 〈-4〉 ⊥ U(2) ⊥ U(2) or 〈-4〉 ⊥ U(2) ⊥ U. Moreover, when H(S, σ; Z) is isomorphic to 〈-4〉 ⊥ U(2) ⊥ U(2), we describe (S, σ) geometrically in terms of a curve of genus two and a Göpel subgroup of its Jacobian.


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Shigeru MUKAI. "Kummer's quartics and numerically reflective involutions of Enriques surfaces." J. Math. Soc. Japan 64 (1) 231 - 246, January, 2012.


Published: January, 2012
First available in Project Euclid: 26 January 2012

zbMATH: 1237.14046
MathSciNet: MR2879743
Digital Object Identifier: 10.2969/jmsj/06410231

Primary: 14J28
Secondary: 14K10 , 32G20

Keywords: Enriques surface , Kummer surface , period

Rights: Copyright © 2012 Mathematical Society of Japan

Vol.64 • No. 1 • January, 2012
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