Advertisement

Maximal Families of CMCY Type

  • Jan Christian RohdeEmail author
Chapter
  • 733 Downloads
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.

Keywords

Elliptic Curf Hyperbolic Plane Rational Curf Hodge Structure Symmetric Domain 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Copyright information

© Springer-Verlag Berlin Heidelberg 2009

Authors and Affiliations

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

Personalised recommendations