Maximal Families of CMCY Type

  • Jan Christian RohdeEmail author
Part of the Lecture Notes in Mathematics book series (LNM, volume 1975)

In this chapter we use the classification of involutions on K3 surfaces S by V. V. Nikulin [51], which act by ?1 on H0(S, ωS). If the divisor of fixed points consists at most of rational curves, the Borcea-Voisin construction yields a maximal holomorphic CMCY family of 3-manifolds.

After we have recalled some basic facts in Section 11.1, we define a Shimura datum by using involutions on the integral lattice in Section 11.2. Each of the points of a dense open subset of the bounded symmetric domain obtained from this Shimura datum represents a marked K3 surface with involution. By using this fact, we obtain our examples of maximal holomorphic CMCY families of 3-manifolds in Section 11.3. For each n ε N with n ≤ 11 there is a holomorphic maximal CMCY family over a basis of dimension n.


Elliptic Curf Hyperbolic Plane Rational Curf Hodge Structure Symmetric Domain 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2009

Authors and Affiliations

  1. 1.Institut fuer Algebraische Geometrie Leibniz Universität Hannover Welfengarten 1, GRK 1463HannoverGermany

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