- Turkish Journal of Mathematics
- Vol: 42 Issue: 4
- Combinatorial enumeration of cyclic covers of $\mathbb{P}^{1}$
Combinatorial enumeration of cyclic covers of $\mathbb{P}^{1}$
Authors : Alberto Besana, Cristina Martinez Ramirez
Pages : 2018-2034
View : 7 | Download : 5
Publication Date : 9999-12-31
Article Type : Makaleler
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