1 results
Counting Higgs bundles and type
$A$ quiver bundles
- Part of
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- Journal:
- Compositio Mathematica / Volume 156 / Issue 4 / April 2020
- Published online by Cambridge University Press:
- 27 February 2020, pp. 744-769
- Print publication:
- April 2020
-
- Article
- Export citation
-
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.
