arXiv subjects

A. Nozad

Publications and source records attributed to A. Nozad.

2 recordsLinked to original sources

arXiv2018

Homotopy Type of Moduli Spaces of G-Higgs Bundles and Reducibility of the Nilpotent Cone

Let $G$ be a real reductive Lie group, and $H^{\mathbb{C}}$ the complexification of its maximal compact subgroup $H\subset G$. We consider classes of semistable $G$-Higgs bundles over a Riemann surface $X$ of genus $g\geq2$ whose underlying $H^{\mathbb{C}}$-principal bundle is unstable. This allows us to find obstructions to a deformation retract from the moduli space of $G$-Higgs bundles over $X$ to the moduli space of $H^{\mathbb{C}}$-bundles over $X$, in contrast with the situation when $g=1$, and to show reducibility of the nilpotent cone of the moduli space of $G$-Higgs bundles, for $G$ complex.

math.AG↗

arXiv2018

Quiver Bundles and Wall Crossing for Chains

Holomorphic chains on a Riemann surface arise naturally as fixed points of the natural C*-action on the moduli space of Higgs bundles. In this paper we associate a new quiver bundle to the Hom-complex of two chains, and prove that stability of the chains implies stability of this new quiver bundle. Our approach uses the Hitchin-Kobayashi correspondence for quiver bundles. Moreover, we use our result to give a new proof of a key lemma on chains (due to Álvarez-Cónsul, García-Prada and Schmitt), which has been important in the study of Higgs bundle moduli; this proof relies on stability and thus avoids the direct use of the chain vortex equations.

math.AG↗