Details
| Original language | English |
|---|---|
| Pages (from-to) | 3001-3022 |
| Number of pages | 22 |
| Journal | Geometry and Topology |
| Volume | 28 |
| Issue number | 7 |
| Publication status | Published - 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
- Mathematics(all)
- Geometry and Topology
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In: Geometry and Topology, Vol. 28, No. 7, 25.11.2024, p. 3001-3022.
Research output: Contribution to journal › Article › Research › peer review
}
TY - JOUR
T1 - Holomorphic 1–forms on the moduli space of curves
AU - Favale, Filippo Francesco
AU - Pirola, Gian Pietro
AU - Torelli, Sara
N1 - Publisher Copyright: © 2024 Mathematical Sciences Publishers.
PY - 2024/11/25
Y1 - 2024/11/25
N2 - 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.
AB - 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.
KW - 1–forms
KW - extension of sections
KW - moduli space
KW - positivity
UR - http://www.scopus.com/inward/record.url?scp=85200046185&partnerID=8YFLogxK
U2 - 10.48550/arXiv.2009.10490
DO - 10.48550/arXiv.2009.10490
M3 - Article
VL - 28
SP - 3001
EP - 3022
JO - Geometry and Topology
JF - Geometry and Topology
SN - 1465-3060
IS - 7
ER -