Combinatorial enumeration of cyclic covers of $\mathbb{P}^{1}$

Authors: ALBERTO BESANA, CRISTINA MARTINEZ RAMIREZ

Abstract: We study plane algebraic curves defined over a field $k$ of arbitrary characteristic that are ramified coverings of the projective line $\mathbb{P}^{1}(k)$ branched over a given configuration of distinct points by their ramification type specified by a partition of $d$ the degree of the covering. We enumerate them by using the combinatorics of partitions and its connection to the representation theory of the symmetric group.

Keywords: Algebraic curve, covering, symmetric group

Full Text: PDF