Strebel differentials on stable curves and Kontsevich's proof of Witten's conjecture

Details Strebel differentials on stable curves and Kontsevich's proof of Witten's conjecture Strebel differentials on stable curves and Kontsevich's proof of Witten's conjecture

2002-09-06

arxiv.org/abs/math/0209071v2

Mathematics

Algebraic Geometry

45 pages, 9 figures. A significantly extended version

Scientific paper

We define Strebel differentials for stable complex curves, prove the
existence and uniqueness theorem that generalizes Strebel's theorem for smooth
curves, prove that Strebel differentials form a continuous family over the
moduli space of stable curves, and show how this construction can be applied to
clarify a delicate point in Kontsevich's proof of Witten's conjecture.

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