Holomorphic differential forms on moduli spaces of stable curves

被引：0

作者：

Fontanari, Claudio ^{[1
]}

机构：

[1] Univ Trento, Dipartimento Matemat, Via Sommarive 14, I-38123 Trento, Italy

来源：

GEOMETRIAE DEDICATA | 2024年 / 218卷 / 01期

关键词：

Moduli spaces; Stable curves; Holomorphic differential forms; Hodge numbers; Cohomology groups; DIMENSION;

D O I：

10.1007/s10711-023-00851-6

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We prove that the space of holomorphic p-forms on the moduli space M <overbar> </mml:mover> 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 <mml:mo>= 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.

引用

页数：4

共 11 条

[1] Arbarello E, 1998, PUBL MATH-PARIS, P97
[2] On the birational geometry of moduli spaces of pointed curves
Ballico, Edoardo
Casnati, Gianfranco
Fontanari, Claudio
[J]. FORUM MATHEMATICUM, 2009, 21 (05) : 935 - 950
[3] Bergstrom J., Ann. Math.
[4] Moduli of curves and spin structures via algebraic geometry
Bini, G
Fontanari, C
[J]. TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 2006, 358 (07) : 3207 - 3217
[5] The eleventh cohomology group of Mg,n
Canning, Samir
Larson, Hannah
Payne, Sam
[J]. FORUM OF MATHEMATICS SIGMA, 2023, 11
[6] Faber C., 2013, Adv. Lect. Math. (ALM), V24, P293
[7] THE VIRTUAL COHOMOLOGICAL DIMENSION OF THE MAPPING CLASS GROUP OF AN ORIENTABLE SURFACE
HARER, JL
[J]. INVENTIONES MATHEMATICAE, 1986, 84 (01) : 157 - 176
[8] INTERSECTION THEORY OF MODULI SPACE OF STABLE N-POINTED CURVES OF GENUS ZERO
KEEL, S
[J]. TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 1992, 330 (02) : 545 - 574
[9] The Kodaira dimension of moduli spaces of curves with marked points
Logan, A
[J]. AMERICAN JOURNAL OF MATHEMATICS, 2003, 125 (01) : 105 - 138
[10] Tautological rings of spaces of pointed genus two curves of compact type
Petersen, Dan
[J]. COMPOSITIO MATHEMATICA, 2016, 152 (07) : 1398 - 1420

← 1 2 →