Relative moduli spaces of complex structures: an example
| dc.creator | Burman, Yurii M. | |
| dc.date | 1999-03-04 | |
| dc.date.accessioned | 2026-07-07T05:28:13Z | |
| dc.date.available | 2026-07-07T05:28:13Z | |
| dc.description | Let M and N be even-dimensional oriented real manifolds, and $u:M \to N$ be a smooth mapping. A pair of complex structures at M and N is called u-compatible if the mapping u is holomorphic with respect to these structures. The quotient of the space of u-compatible pairs of complex structures by the group of u-equivariant pairs of diffeomorphisms of M and N is called a moduli space of u-equivariant complex structures. The paper contains a description of the fundamental group G of this moduli space in the following case: $N = CP^1, M \subset CP^2$ is a hyperelliptic genus g curve given by the equation $y^2 = Q(x)$ where Q is a generic polynomial of degree 2g+1, and $u(x,y) = y^2$. The group G is a kernel of several (equivalent) actions of the braid-cyclic group $BC_{2g}$ on 2g strands. These are: an action on the set of trees with 2g numbered edges, an action on the set of all splittings of a (4g+2)-gon into numbered nonintersecting quadrangles, and an action on a certain set of subgroups of the free group with 2g generators. $G_{2g} \subset BC_{2g}$ is a subgroup of the index $(2g+1)^{2g-2}$. Key words: Teichmüller spaces, Lyashko-Looijenga map, braid group. | |
| dc.description | 21 pages, 3 figures, LaTeX with epsf macros. To be published in the Proceedings of Arnold's Seminar, AMS, 1999 | |
| dc.identifier | https://arxiv.org/abs/math/9903029 | |
| dc.identifier | http://arxiv.org/abs/math/9903029 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/78177 | |
| dc.subject | Differential Geometry | |
| dc.subject | Combinatorics | |
| dc.title | Relative moduli spaces of complex structures: an example | |
| dc.type | text |