Holomorphic 1–forms on the moduli space of curves

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Authors

  • Filippo Francesco Favale
  • Gian Pietro Pirola
  • Sara Torelli

Research Organisations

External Research Organisations

  • University of Pavia
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Details

Original languageEnglish
Pages (from-to)3001-3022
Number of pages22
JournalGeometry and Topology
Volume28
Issue number7
Publication statusPublished - 25 Nov 2024

Abstract

Since the 1960s it has been well known that there are no nontrivial closed holomorphic 1–forms on the moduli space Mg of smooth projective curves of genus g > 2. We strengthen this result, proving that for g 5 there are no nontrivial holomorphic 1–forms. With this aim, we prove an extension result for sections of locally free sheaves F on a projective variety X. More precisely, we give a characterization for the surjectivity of the restriction map Formula presented for divisors D in the linear system of a sufficiently large multiple of a big and semiample line bundle L. Then we apply this to the line bundle L given by the Hodge class on the Deligne–Mumford compactification of Mg.

Keywords

    1–forms, extension of sections, moduli space, positivity

ASJC Scopus subject areas

Cite this

Holomorphic 1–forms on the moduli space of curves. / Favale, Filippo Francesco; Pirola, Gian Pietro; Torelli, Sara.
In: Geometry and Topology, Vol. 28, No. 7, 25.11.2024, p. 3001-3022.

Research output: Contribution to journalArticleResearchpeer review

Favale FF, Pirola GP, Torelli S. Holomorphic 1–forms on the moduli space of curves. Geometry and Topology. 2024 Nov 25;28(7):3001-3022. doi: 10.48550/arXiv.2009.10490, 10.2140/gt.2024.28.3001
Favale, Filippo Francesco ; Pirola, Gian Pietro ; Torelli, Sara. / Holomorphic 1–forms on the moduli space of curves. In: Geometry and Topology. 2024 ; Vol. 28, No. 7. pp. 3001-3022.
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