Counting Higgs bundles and type A quiver bundles

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.