Stable Higgs \(G\)-sheaves
A Higgs bundle over a projective scheme \(X\) is a vector bundle \(E\), together with a homomorphism \(\theta: E\to E\otimes\Omega_X\), such that \(\theta\wedge\theta=0\). The authors extend this notion of Higgs bundles to principal \(G\)-sheaves on a smooth projective complex scheme \(X\) of any dimension, where \(G\) is an arbitrary reductive structure group. The starting point is a principal \(G\)-sheaf \(P\) over a torsion free sheaf \(E\). The authors define a \(G\)-Higgs field on \(P\) by means of a homomorphism \(\Theta:E\oplus(\zeta \otimes \mathcal O_X)\), where \(\zeta\) is the center. Then the authors define the wedge product \(\Theta\wedge\Theta\) by extending sections arising from a natural exact sequence. Higgs \(G\)-sheaves are \(G\)-sheaves for which \(\Theta\wedge\Theta=0\). The notion of semistability for Higgs \(G\)-fields is introduced by means of compatibility with orthogonal algebra filtrations on \(E\). The authors prove the existence of a quasi-projective coarse moduli space of classes of semistable Higgs \(G\)-sheaves, with fixed numerical invariants.
scientific article; zbMATH DE number 5361880
scientific article