1205.6728 (S. A. H. Cardona)

Approximate Hermitian-Yang-Mills structures and semistability for Higgs
bundles. II: Higgs sheaves and admissible structures    [PDF]

S. A. H. Cardona

We study the basic properties of Higgs sheaves over compact K\"ahler manifolds and we establish some results concerning the notion of semistability; in particular, we show that any extension of semistable Higgs sheaves with equal slopes is semistable. Then, we use the flattening theorem to construct a regularization of any torsion-free Higgs sheaf and we show that it is in fact a Higgs bundle. Using this, we prove that any Hermitian metric on a regularization of a torsion-free Higgs sheaf induces an admissible structure on the Higgs sheaf. Finally, using admissible structures we proved some properties of semistable Higgs sheaves.

View original: http://arxiv.org/abs/1205.6728