稳定曲线模空间上的全纯微分形式

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

Claudio Fontanari

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引用次数: 0

摘要

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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Holomorphic differential forms on moduli spaces of stable curves

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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