Level structures on the Weierstrass family of cubics
| dc.creator | Bernstein, Mira | |
| dc.creator | Tuffley, Christopher | |
| dc.date | 2005-12-06 | |
| dc.date | 2006-07-03 | |
| dc.date.accessioned | 2026-07-07T08:07:25Z | |
| dc.date.available | 2026-07-07T08:07:25Z | |
| dc.description | Let W -> A^2 be the universal Weierstrass family of cubic curves over C. For each N >= 2, we construct surfaces parametrizing the three standard kinds of level N structures on the smooth fibers of W. We then complete these surfaces to finite covers of A^2. Since W -> A^2 is the versal deformation space of a cusp singularity, these surfaces convey information about the level structure on any family of curves of genus g degenerating to a cuspidal curve. Our goal in this note is to determine for which values of N these surfaces are smooth over (0,0). From a topological perspective, the results determine the homeomorphism type of certain branched covers of S^3 with monodromy in SL_2(Z/N). | |
| dc.description | LaTeX, 12 pages; added section giving a topological interpretation of the results | |
| dc.identifier | https://arxiv.org/abs/math/0512117 | |
| dc.identifier | http://arxiv.org/abs/math/0512117 | |
| dc.identifier | Communications in Algebra, 35:1249--1261, 2007 | |
| dc.identifier | doi:10.1080/00927870601142256 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/130933 | |
| dc.subject | Algebraic Geometry | |
| dc.subject | Geometric Topology | |
| dc.subject | 14D05; 14H20, 57M12 | |
| dc.title | Level structures on the Weierstrass family of cubics | |
| dc.type | text |