The Chevalley-Weil formula on nodal curves

Yubo Tong; Yubo Tong

doi:10.3934/math.2025554

AIMS Mathematics

2025, Volume 10, Issue 5: 12228-12253. doi: 10.3934/math.2025554

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The Chevalley-Weil formula on nodal curves

Yubo Tong ^,

School of Mathematical Sciences, Xiamen University, 361005 Xiamen, China

Received: 06 February 2025 Revised: 02 May 2025 Accepted: 09 May 2025 Published: 27 May 2025
MSC : 14H05, 14H20, 14H37

In this paper, we studied the eigenspace of the regular differentials on a connected nodal curve $ X $ under the action of a finite automorphism group $ G $. We proved that the dimension of the space of $ G $-invariant regular differentials is the arithmetic genus of the quotient nodal curve $ X/G $. In addition, we generalized the Chevalley-Weil formula to nodal curves in the case where $ X/G $ is smooth and gave some examples.
- Chevalley-Weil formula,
- nodal curves,
- regular differentials,
- $ G $-invariant,
- characters
Citation: Yubo Tong. The Chevalley-Weil formula on nodal curves[J]. AIMS Mathematics, 2025, 10(5): 12228-12253. doi: 10.3934/math.2025554

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Abstract

In this paper, we studied the eigenspace of the regular differentials on a connected nodal curve $ X $ under the action of a finite automorphism group $ G $. We proved that the dimension of the space of $ G $-invariant regular differentials is the arithmetic genus of the quotient nodal curve $ X/G $. In addition, we generalized the Chevalley-Weil formula to nodal curves in the case where $ X/G $ is smooth and gave some examples.

References

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