Search results for " coverings"
showing 5 items of 15 documents
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}…
Irreducible components of Hurwitz spaces of coverings with two special fibers
2013
In this paper we prove new results of irreducibility for Hurwitz spaces of coverings whose monodromy group is a Weyl group of type B_d and whose local monodromies are all reflections except two.
On the classification of Kim and Kostrikin manifolds
2006
International audience; We completely classify the topological and geometric structures of some series of closed connected orientable 3-manifolds introduced by Kim and Kostrikin in [20, 21] as quotient spaces of certain polyhedral 3-cells by pairwise identifications of their boundary faces. Then we study further classes of closed orientable 3-manifolds arising from similar polyhedral schemata, and describe their topological properties.
MR 3020148 Reviewed McMullen, C.T. Braid groups and Hodge theory. Mathematische Annalen, vol. 355 (2013), pp.893–-946. (Reviewer Francesca Vetro) 20F…
2014
In this paper, the author studies the unitary representations of the braid group and the geometric structures on moduli space that arise via the Hodge theory of cyclic branched coverings of P^1. In particular, the author is interested in the classification of certain arithmetic subgroups of U(r, s) which envelop the image of the braid group. The author investigates their connections with complex reflection groups, Teichm\"{u}lller curves, ergodic theory and problems in surface topology.
MR 2831984 Reviewed Masuda T. Families of finite coverings of the Riemann sphere. Osaka J. Math. 48 (2011), no. 2, 515--540. (Reviewer Francesca Vetr…
2012
Let $G$ be a finite group and let $H$ be a subgroup of $G$ which does not contain normal subgroups of $G$ except $\{ id \}$. The group $G$ acts on the set of the left coset of $G / H$ as follows: \begin{center} $(g, H a) \rightarrow H a g^{- 1}$. \end{center} The author observes that the action defined above is effective and this gives a permutation representation of $G$, $R: G \rightarrow S_{d}$, where $d =[G : H]$. The condition on $H$ ensures that $R$ is injective. Thus, $G$ can be seen as a transitive subgroup of $S_{d}$. Let $X$ and $ Y$ be connected complex varieties. A finite covering $f: X \rightarrow Y$, which branches at most at $B$, is said a $(G, H)-$coverings if there is a surj…