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Counting Higgs bundles and type quiver bundles
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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.
Title: Counting Higgs bundles and type quiver bundles
Description:
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.
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