A geometric parametrization for the virtual Euler characteristic for the moduli spaces of real and complex algebriac curves
| dc.creator | Goulden, I. P. | |
| dc.creator | Harer, J. L. | |
| dc.creator | Jackson, D. M. | |
| dc.date | 1999-02-05 | |
| dc.date.accessioned | 2026-07-07T05:27:49Z | |
| dc.date.available | 2026-07-07T05:27:49Z | |
| dc.description | We show that the virtual Euler characteristics of the moduli spaces of $s$-pointed algebraic curves of genus $g$ can be determined from a polynomial in $1/γ$ where $γ$ permits specialization, through $γ=1,$ to the complex case treated by Harer and Zagier and, through $γ=1/2$, to the real case. This polynomial appears to have geometric significance, and may be the virtual Euler characteristic of some moduli space, as yet unidentified. This is related to a conjecture that the indeterminate $b=γ^1-1$ is associated with a combinatorial invariant of cell-decompositions through matrix models and the Jack symmetric functions. The development uses Strebel differentials to triangulate the moduli spaces, and the identification of $γ$ both as a parameter in a Jack symmetric function and as a parameter in a matrix model through generalized Selberg integrals. | |
| dc.description | 24 pages | |
| dc.identifier | https://arxiv.org/abs/math/9902044 | |
| dc.identifier | http://arxiv.org/abs/math/9902044 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/78067 | |
| dc.subject | Algebraic Geometry | |
| dc.subject | Combinatorics | |
| dc.subject | 58D29;58C35;05C30;05E05 | |
| dc.title | A geometric parametrization for the virtual Euler characteristic for the moduli spaces of real and complex algebriac curves | |
| dc.type | text |