Generalized intersection pairings on moduli spaces of vector bundles over a curve
Chenjing Bu, Young-Hoon Kiem

TL;DR
This paper introduces a generalized intersection pairing for Artin stacks with proper moduli spaces, compares various existing constructions for moduli of vector bundles over curves, and provides explicit low-rank computations.
Contribution
It establishes wall crossing formulas linking different intersection pairings and offers a unified framework for understanding their relationships.
Findings
Wall crossing formulas relate different intersection pairings.
Explicit computations are provided for low-rank cases.
The framework applies to moduli stacks of semistable bundles over curves.
Abstract
We introduce the notion of a generalized intersection pairing for an Artin stack with a proper good moduli space and nonempty stable part. For the moduli stack of semistable bundles over a smooth projective curve, there are four known constructions by partial desingularization, parabolic bundles, stable pairs and wall crossing. In this paper, we compare all these generalized intersection pairings by establishing wall crossing formulas between them. Explicit computations for low rank cases are included.
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Taxonomy
TopicsAlgebraic Geometry and Number Theory · Algebraic structures and combinatorial models · Geometry and complex manifolds
