Integration on moduli spaces of stable curves through localization
Brad Safnuk
TL;DR
This paper presents a novel localization-based method for computing intersection numbers on moduli spaces of stable curves, providing a new proof of Mirzakhani's recursion for mixed psi and kappa_1 classes.
Contribution
It introduces a new localization technique for intersection calculations on ar{M}_{g,n} and offers a proof of Mirzakhani's recursion relation.
Findings
New localization method for intersection theory
Proof of Mirzakhani's recursion relation
Enhanced computational approach for moduli space intersections
Abstract
We introduce a new method of calculating intersections on \bar{M}_{g,n}, using localization of equivariant cohomology. As an application, we give a proof of Mirzakhani's recursion relation for calculating intersections of mixed psi and kappa_1 classes.
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Taxonomy
TopicsAlgebraic Geometry and Number Theory · Topological and Geometric Data Analysis · Advanced Combinatorial Mathematics