Signatures of alternating group actions with non-zero quotient genus

2025/09/24 by Paulhus, Jennifer, Wootton, Aaron
#14H37 #20B05 #20D06 #30F20 #Algebraic Geometry (math.AG) #FOS: Mathematics #Group Theory (math.GR)

paper · doi:10.48550/arxiv.2509.19692

Abstract

We classify up to signature all the ways the alternating group A_n can act on a compact Riemann surfaces when the quotient genus is greater than 0. In particular, we prove that for A_n with n>6 every potential signature for the group acting with quotient genus greater than 0 is an actual signature. We also show that in the case of n=5, respectively n=6, the only failure is for [1;2], respectively [1;3]. Along the way we also prove that for any finite simple non-abelian group, all potential signatures with quotient genus greater than 1 are actual signatures.

Citations

• Non-Abelian Simple Groups Act with Almost All Signatures

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