arXiv subjects

Lucas de Amorin

Publications and source records attributed to Lucas de Amorin.

3 recordsLinked to original sources

arXiv2025

Motivic Mirror Symmetry for Character Stacks

We propose a motivic version of T. Hausel and M. Thaddeus' Topological Mirror Symmetry for character stacks associated with arbitrary semisimple groups, which is an analogue of F. Loeser and D. Wyss' result for Chow motives of moduli spaces of Higgs bundles. As first steps towards it, we generalize A. Mellit's cell decomposition to arbitrary connected and reductive groups. We use it to describe all automorphisms on the associated character stacks. Then we show that the Weil pairing induces a duality between cells that interchanges automorphisms by connected components. As a toy example, we show that these results imply our conjecture for the special linear group of rank two.

math.AG↗

arXiv2025

On the motive of quotients of induced actions

We explore computational tools that allow to compute the class on the Grothendieck ring of varieties of finite cyclic quotients in some interesting examples. As an main application, we determine the motive of low rank representation varieties associated with torus knots and general linear groups using an equivariant analogue of the strategy for special linear groups due to A.González-Prieto and V.Muñoz.

math.AG↗

arXiv2024

Counting stringy points on a family of character varieties

We provided explicit formulas for the number of stringy points over finite fields of parabolic type A character varieties with generic semisimple monodromy. This leads to formulas for their stringy E-polynomials. In particular, they satisfy the Betti Topological Mirror Symmetry Conjecture of T. Hausel and M. Thaddeus, as well as a refinement regarding isotypic components. Our proof is based on a Frobenius' type formula for Clifford's type settings and an analysis of it in a specific set-up related to regular wreath products with cyclic groups.

math.AG↗