arXiv subjects

Emanuel Roth

Publications and source records attributed to Emanuel Roth.

2 recordsLinked to original sources

arXiv2026

Jordan-Hölder theory for complementary polyhedra and moduli of parahoric Higgs torsors

We extend Behrend's theory of complementary polyhedra to include Jordan-Hölder theory. This provides a uniform approach to describing the Jordan-Hölder filtrations and S-equivalence in moduli stacks of bundles, following Zhang. As an application, we give a description of Jordan-Hölder reductions and S-equivalence in the semistable locus of parahoric torsors and parahoric Higgs torsors, coming from their good moduli spaces constructed by Alper-Halpern-Leistner-Heinloth and Réga. This application uses the Rees construction to identify filtrations of moduli stacks with reductions of bundles, and induces a Jordan-Hölder stratification of the moduli stacks.

math.AG↗

arXiv2026

Harder-Narasimhan filtrations of decorated vector bundles

A decorated vector bundle is a vector bundle equipped with a reduction of structure group to a complex reductive subgroup $G \subseteq \mathbf{GL}(r,\mathbb{C})$. Examples include symplectic and special-orthogonal vector bundles, as well as vector bundles with trivial determinants. In this expository paper, we provide direct constructions of Harder-Narasimhan filtrations of symplectic and special-orthogonal vector bundles, and use them to construct canonical reductions in the sense of Atiyah and Bott. We compare these canonical reductions to those constructed by Biswas and Holla. Lastly, we set up the obstruction theory necessary to define Harder-Narasimhan types of principal bundles, and stratify the moduli stack of principal $G$-bundles.

math.AG↗