Finiteness of Subfamilies of Calabi-Yau n-Folds over Curves with Maximal Length of Yukawa-Coupling

Details Finiteness of Subfamilies of Calabi-Yau n-Folds over Curves with Maximal Length of Yukawa-Coupling Finiteness of Subfamilies of Calabi-Yau n-Folds over Curves with Maximal Length of Yukawa-Coupling

2010-10-20

arxiv.org/abs/1010.4141v1

Mathematics

Algebraic Geometry

9 pages

Scientific paper

We give a simplified and more algebraic proof of the finiteness of the
families of Calabi-Yau n-folds with non-vanishing of Yukawa-coupling over a
fixed base curve and with fixed degeneration locus. We also give a
generalization of this result. Our method is variation of Hodge structure and
poly-stability of Higgs bundles.

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