Holomorphic differential forms on moduli spaces of stable curves

2023/06/12 by Claudio Fontanari, Fontanari, Claudio · 1 citation
Mathematics · #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Geometry and complex manifolds

paper · pdf · doi:10.48550/arxiv.2306.06978

openalex publication_date 2023/06/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We prove that the space of holomorphic p-forms on the moduli space M_g,n of stable curves of genus g with n marked points vanishes for p=14, 16, 18 unconditionally and also for p=20 under a natural assumption in the case g=3. This result is consistent with the Langlands program and it is obtained by applying the Arbarello-Cornalba inductive approach to the cohomology of moduli spaces.

Cited by

• FA-modules of holomorphic forms on M_g,n

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