Journal of the Mathematical Society of Japan
Online ISSN : 1881-1167
Print ISSN : 0025-5645
ISSN-L : 0025-5645
Kummer's quartics and numerically reflective involutions of Enriques surfaces
Shigeru Mukai
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2012 年 64 巻 1 号 p. 231-246

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抄録
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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© 2012 The Mathematical Society of Japan
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