Holomorphic differential forms on moduli spaces of stable curves

IF 0.5 4区数学 Q3 MATHEMATICS

Geometriae Dedicata Pub Date : 2023-10-24 DOI:10.1007/s10711-023-00851-6

Claudio Fontanari

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引用次数: 0

Abstract

Abstract We prove that the space of holomorphic p -forms on the moduli space $$\overline{\mathcal {M}}_{g,n}$$ M ¯ g , n of stable curves of genus g with n marked points vanishes for $$p=14, 16, 18$$ p = 14 , 16 , 18 unconditionally and also for $$p=20$$ p = 20 under a natural assumption in the case $$g=3$$ 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.

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稳定曲线模空间上的全纯微分形式

摘要证明了在模空间$$\overline{\mathcal {M}}_{g,n}$$ M¯g, n上有n个标记点的g属稳定曲线的全纯p -形式空间对于$$p=14, 16, 18$$ p = 14,16,18无条件地消失，对于$$p=20$$ p = 20在一个自然假设下$$g=3$$ g = 3也无条件地消失。这一结果与Langlands规划一致，并通过对模空间上同调的Arbarello-Cornalba归纳方法得到。

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来源期刊

Geometriae Dedicata 数学-数学

CiteScore

0.90

自引率

0.00%

发文量

审稿时长

4-8 weeks

期刊介绍： Geometriae Dedicata concentrates on geometry and its relationship to topology, group theory and the theory of dynamical systems. Geometriae Dedicata aims to be a vehicle for excellent publications in geometry and related areas. Features of the journal will include: A fast turn-around time for articles. Special issues centered on specific topics. All submitted papers should include some explanation of the context of the main results. Geometriae Dedicata was founded in 1972 on the initiative of Hans Freudenthal in Utrecht, the Netherlands, who viewed geometry as a method rather than as a field. The present Board of Editors tries to continue in this spirit. The steady growth of the journal since its foundation is witness to the validity of the founder''s vision and to the success of the Editors'' mission.