Search results for " cyclic coverings."

MR 3219513 Reviewed Venkataramana T. N. Monodromy of cyclic coverings of the projective line. Invent. Math., 197 (2014), 1–-45. (Reviewer Francesca V…

2014

Let $d \geq 2$ and $n \geq 1$ be integers and $P_{n+1}$ be the pure braid group on $n + 1$ strands. In this paper, the author studies the image of $P_{n+1}$ under the monodromy action on the homology of a cyclic covering of degree $d$ of the projective line. More precisely, let $k_{1}, \ldots, k_{n + 1}$ be integers such that $1 \leq k_{i} \leq d - 1$ and gcd$(k_{i}, d) = 1$ for each $i$. Moreover, let $a_{1}, \ldots, a_{n + 1}$ be distinct points of the complex plane and $C$ be the space of points in $\mathbb{C}^{n + 1}$ with all distinct coordinates. Let us denote by $X_{a, k}$ the affine curve defined by the equation $$ y^{d} = (x - a_{1})^{k_{1}} (x - a_{2})^{k_{2}} \cdots (x - a_{n +1}…