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

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Abstract

Let S be a complex algebraic K3 surface. It is proved that the 0-dimensional cusps of the Kähler moduli of S are in one-to-one correspondence with the twisted Fourier-Mukai partners of S. As a result, a counting formula for the 0-dimensional cusps of the Kähler moduli is obtained. Applications to rational maps between K3 surfaces are given. When the Picard number of S is 1, the bijective correspondence is calculated explicitly by using the Fricke modular curve.

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  1. Graduate School of Mathematical Sciences, University of Tokyo, Tokyo, 153-8914, Japan

    Shouhei Ma

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  1. Shouhei Ma
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Ma, S. On the 0-dimensional cusps of the Kähler moduli of a K3 surface. Math. Ann. 348, 57–80 (2010). https://doi.org/10.1007/s00208-009-0466-x

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  • DOI: https://doi.org/10.1007/s00208-009-0466-x

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