Critical groups in harmonic abelian quotients

2024/09/06 by Vetluzhskikh, Mariia, Zakharov, Dmitry
#05C31 #14H40 #Algebraic Geometry (math.AG) #Combinatorics (math.CO) #FOS: Mathematics

paper · doi:10.48550/arxiv.2409.04629

Abstract

A harmonic cover of graphs p:\widetildeX→ X induces a surjective pushforward morphism p_*:Jac(\widetildeX)→ Jac(X) on the critical groups. In the case when p is Galois with abelian Galois group, we compute the order of the kernel of p_*, and hence the relationship between the numbers of spanning trees of \widetildeX and X, in terms of Zaslavsky's bias matroid associated to the cover p:\widetildeX→ X.

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