Abstract
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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