Counting Higgs bundles and type \(A\) quiver bundles. (English) Zbl 1514.14011
Summary: 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 twisting line bundle degree is at least \(2g-2\) (this includes the case of usual Higgs bundles). This yields a closed expression for the Donaldson-Thomas invariants of the moduli spaces of twisted Higgs bundles. We similarly deal with twisted quiver sheaves of type \(A\) (finite or affine), obtaining in particular a Harder-Narasimhan-type formula counting semistable \(U(p,q)\)-Higgs bundles over a smooth projective curve defined over a finite field.
MSC:
| 14D20 | Algebraic moduli problems, moduli of vector bundles |
| 16G20 | Representations of quivers and partially ordered sets |
| 14N35 | Gromov-Witten invariants, quantum cohomology, Gopakumar-Vafa invariants, Donaldson-Thomas invariants (algebro-geometric aspects) |
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