On the 0-dimensional cusps of the Kahler moduli of a K3 surface

Details On the 0-dimensional cusps of the Kahler moduli of a K3 surface On the 0-dimensional cusps of the Kahler moduli of a K3 surface

2008-12-22

arxiv.org/abs/0812.4132v2

Mathematics

Algebraic Geometry

24pages

Scientific paper

10.1007/s00208-009-0466-x

Let S be a projective K3 surface. It is proved that the 0-dimensional cusps of the Kahler moduli of S are in one-to-one correspondence with the twisted Fourier-Mukai partners of S. This leads to a counting formula for the 0-dimensional cusps of the Kahler moduli. Applications to rational maps between K3 surfaces with large Picard numbers are given. When the Picard number of S is 1, the bijective correspondence is calculated explicitly.

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