Higgs bundles over P^1 and quiver representations
Sergey Mozgovoy
TL;DR
This paper derives an explicit formula for invariants of moduli spaces of twisted Higgs bundles over P^1 and connects these to quiver representation invariants, facilitating computations and supporting existing conjectures.
Contribution
It provides a new explicit formula linking Higgs bundle invariants to quiver representation invariants, enabling easier calculations and validation of conjectures.
Findings
Formula aligns with existing conjectures
Facilitates computational implementation
Connects Higgs bundles with quiver representations
Abstract
In this note we prove a new explicit formula for the invariants of moduli spaces of twisted Higgs bundles over P^1 and we relate these invariants to the invariants of moduli spaces of representations of some infinite symmetric quiver. The formula can be easily implemented for computations and it is in agreement with the existing conjectures for the invariants of twisted Higgs bundles over curves. Results of this note were presented in Oberwolfach in May 2014.
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Taxonomy
TopicsAlgebraic structures and combinatorial models · Algebraic Geometry and Number Theory · Advanced Algebra and Geometry