Counts of maps to Grassmannians and intersections on the moduli space of bundles

2006/02/15 by Alina Marian, Marian, Alina, Dragos Oprea +1 · 1 citation
Mathematics · #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #math.AG

paper · pdf · doi:10.48550/arxiv.math/0602335

openalex publication_date 2006/02/15 · arxiv created 2006/02/27 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We show that intersection numbers on the moduli space of stable bundles of coprime rank and degree over a smooth complex curve can be recovered as highest-degree asymptotics in formulas of Vafa-Intriligator type. In particular, we explicitly evaluate all intersection numbers appearing in the Verlinde formula. Our results are in agreement with previous computations of Witten, Jeffrey-Kirwan and Liu. Moreover, we prove the vanishing of certain intersections on a suitable Quot scheme which can be interpreted as giving equations between counts of maps to the Grassmannian.

Citations

• Two Dimensional Gauge Theories Revisited

Cited by

• A Vafa-Intriligator formula for semi-positive quotients of linear spaces

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