Counting Higgs bundles and type A quiver bundles

Abstract

We prove a closed formula counting semistable twisted (or meromorphic) Higgs bundles of fixed rank and degree over a smooth projective curve of genus g, defined over a finite field, when the degree of the twisting line bundle is at least 2g-2; this includes the case of usual Higgs bundles. We obtain at the same time a closed expression for the Donaldson-Thomas invariants of the moduli spaces of twisted Higgs bundles. We similarly deal with twisted quiver bundles of type A (affine or finite), obtaining in particular a Harder-Narasimhan-type formula counting semistable U(p,q)-bundles over any smooth projective curve over a finite field.

Improved version of arXiv:1411.2101 to now include the case of type A quiver bundles as well. 22 pages

References in corpus (1)

• A computational criterion for the Kac conjecture

Cited by in corpus (5)

• Cohomological $\chi$-independence for moduli of one-dimensional sheaves and moduli of Higgs bundles
• A lax monoidal Topological Quantum Field Theory for representation varieties
• Irreducible components of the global nilpotent cone
• BPS cohomology for rank 2 degree 0 Higgs bundles (and more)
• Counting Parabolic Principal G-bundles with Nilpotent Sections over ${\mathbb{P}}^1$