Quasi-Hodge Metrics and Canonical Singularities

Details Quasi-Hodge Metrics and Canonical Singularities Quasi-Hodge Metrics and Canonical Singularities

2002-11-29

arxiv.org/abs/math/0211456v1

Math. Res. Lett. 10 (2003), 57-70

Mathematics

Algebraic Geometry

15 pages, LaTeX. To appear in Mathematical Research Letters

Scientific paper

We study one parameter degenerations of complex projective manifolds by introducing certain type of Hodge metrics coming from the pluricanonical forms. We show that degenerations with at most canonical singularities are all in the finite distance boundary of moduli spaces. We also propose the converse to be true in the sense that finite distance degenerations admit birational models which have at most canonical singularities in the degenerate fiber. We verify this for curves and show that the Calabi-Yau case follows from the minimal model conjecture.

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