Intersection Theory of Hyperquot Schemes on curves
Riccardo Ontani, Shubham Sinha, Weihong Xu
TL;DR
This paper develops a virtual intersection theory for Hyperquot schemes on curves, extending known formulas and providing explicit counts of maps to flag varieties.
Contribution
It generalizes the Vafa--Intriligator formula to Hyperquot schemes and derives a closed formula for virtual counts of curve maps to partial flag varieties.
Findings
Generalized Vafa--Intriligator formula for Hyperquot schemes
Derived a closed formula for virtual counts of maps to flag varieties
Extended intersection theory to new geometric settings
Abstract
We study the virtual intersection theory of Hyperquot schemes parameterizing sequences of quotient sheaves of a vector bundle on a smooth projective curve. Our results generalize the Vafa--Intriligator formula for Quot schemes and provide a closed formula for virtual counts of maps from the curve to a partial flag variety.
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Taxonomy
TopicsAlgebraic Geometry and Number Theory · Algebraic structures and combinatorial models · Polynomial and algebraic computation