The Chevalley-Weil formula on nodal curves

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.