Topological Recursion Relations by Localization
Algebraic Geometry
2012-06-18 v2
Abstract
Let M_{g,n} be the moduli space of stable genus g curves with n marked points. M_{g,n} has boundary strata consisting of nodal curves. The fundamental classes of these boundary strata may be linearly dependent in the Chow group A_*(M_{g,n}). Relations among these boundary strata can be found by exploiting a localization trick involving stable maps to P^1. This note explains this trick and applies it to give a new derivation of Getzler's relation among codimension 2 boundary strata in M_{1,4}.
Cite
@article{arxiv.math/0310050,
title = {Topological Recursion Relations by Localization},
author = {Eric Edward Katz},
journal= {arXiv preprint arXiv:math/0310050},
year = {2012}
}
Comments
14 pages, 15 Postscript figures, 3 pictex figures; not to be published; the June 2012 update fixes the annoying spelling error in the title and nothing else