Degenaration of Calabi-Yau Manifold with W-P Metric

Details Degenaration of Calabi-Yau Manifold with W-P Metric Degenaration of Calabi-Yau Manifold with W-P Metric

1995-07-28

arxiv.org/abs/alg-geom/9507016v1

Mathematics

Algebraic Geometry

AMSTeX, 27 pages

Scientific paper

In this paper we focus on determining for which degenerations the central fibre is at finite distance with respect to Weil-Petersson metric. We obtain a simple condition on the limiting mixed Hodge structure. Then we combine the result with the canonical mixed Hodge structure of the central fibre and obtain a simple cohomological condition for the central fibre to be at finite distance. As a corollary, we prove that a central fibre with simple nodes is at finite distance. This issue has been raised in the Physics literature including the recent development of so-called "mass-less black holes".

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