Monodromy Groups of Hurwitz-type Problems
| dc.creator | Allcock, Daniel | |
| dc.creator | Hall, Chris | |
| dc.date | 2008-03-03 | |
| dc.date.accessioned | 2026-07-07T09:24:21Z | |
| dc.date.available | 2026-07-07T09:24:21Z | |
| dc.description | We solve the Hurwitz monodromy problem for degree-4 covers. That is, the Hurwitz space H_{4,g} of all simply branched covers of P^1 of degree 4 and genus g is an unramified cover of the space P_{2g+6} of (2g+6)-tuples of distinct points in P^1. We determine the monodromy of pi_1(P_{2g+6}) on the points of the fiber. This turns out to be the same problem as the action of pi_1(P_{2g+6}) on a certain local system of Z/2-vector spaces. We generalize our result by treating the analogous local system with Z/N coefficients, gcd(3,N)=1, in place of Z/2. This in turn allows us to answer a question of Ellenberg concerning families of Galois covers of P^1 with deck group (Z/N)^2:S_3. | |
| dc.description | 15 pages, 2 figures | |
| dc.identifier | https://arxiv.org/abs/0803.0237 | |
| dc.identifier | http://arxiv.org/abs/0803.0237 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/156065 | |
| dc.subject | Group Theory | |
| dc.subject | Commutative Algebra | |
| dc.subject | Algebraic Geometry | |
| dc.subject | 14D05, 14H30, 20B25, 57M10 | |
| dc.title | Monodromy Groups of Hurwitz-type Problems | |
| dc.type | text |