• Corpus ID: 254685542

BPS Lie algebras for totally negative 2-Calabi-Yau categories and nonabelian Hodge theory for stacks

  title={BPS Lie algebras for totally negative 2-Calabi-Yau categories and nonabelian Hodge theory for stacks},
  author={Ben Davison and Lucien Hennecart and Sebastian Schlegel Mejia},
We define and study a sheaf-theoretic cohomological Hall algebra for suitably geometric Abelian categories $\mathcal{A}$ of homological dimension at most two, and a sheaf-theoretic BPS algebra under the conditions that $\mathcal{A}$ is 2-Calabi-Yau and has a good moduli space. We show that the BPS algebra for the preprojective algebra $\Pi_Q$ of a totally negative quiver is the free algebra generated by the intersection cohomology of the closure of the locus parameterising simple $\Pi_Q… 

Cohomological $\chi$-independence for Higgs bundles and Gopakumar-Vafa invariants

The aim of this paper is two-fold: Firstly, we prove Toda's $\chi$-independence conjecture for Gopakumar--Vafa invariants of arbitrary local curves. Secondly, following Davison's work, we introduce

Nonabelian Hodge theory for stacks and a stacky P=W conjecture

Rational singularities for moment maps of totally negative quivers

We prove that the zero-fiber of the moment map of a totally negative quiver has rational singularities. Our proof consists in generalizing dimension bounds on jet spaces of this fiber, which were

BPS algebras and generalised Kac-Moody algebras from 2-Calabi-Yau categories

  • Ben DavisonLucien HennecartSebastian Schlegel Mejia
  • Mathematics
  • 2023
We determine the structure of the BPS algebra of 2-Calabi-Yau Abelian categories whose stack of objects admits a good moduli space. We prove that this algebra is isomorphic to the positive part of

On geometric realizations of the unipotent enveloping algebra of a quiver

We compare and generalize the different geometric constructions of the unipotent generalized Kac-Moody algebra associated to an arbitrary quiver. They happen to be connected to each other by