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

2002/09/06 by Dimitri Zvonkine, Zvonkine, Dimitri · 2 citations
Mathematics · #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Analytic and geometric function theory #FOS: Mathematics #math.AG

paper · pdf · doi:10.48550/arxiv.math/0209071

45 pages, 9 figures. A significantly extended version

openalex publication_date 2002/09/06 · arxiv created 2004/01/07 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

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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