On some lattice computations related to moduli problems

Details On some lattice computations related to moduli problems On some lattice computations related to moduli problems

2010-08-30

arxiv.org/abs/1008.5027v1

Mathematics

Algebraic Geometry

With an appendix by V. Gritsenko

Scientific paper

We show how to solve computationally a combinatorial problem about the possible number of roots orthogonal to a vector of given length in $E_8$. We show that the moduli space of K3 surfaces with polarisation of degree 2d is also of general type for d=52. This case was omitted from the earlier work of Gritsenko, Hulek and the second author. We also apply this method to some related problems. In Appendix A, V. Gritsenko shows how to arrive at the case d=52 and some others directly.

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