Seminar

Geometry Seminar

The moduli stack of principal ρ-sheaves and Gieseker-Harder-Narasimhan filtrations

Speaker:  Alfonso Zamora (UPM)
Date:  Wednesday, 01 June 2022 - 15:30
Place:  Aula Naranja, ICMAT

Abstract:

Given a smooth projective variety X and a connected reductive group G defined over a field of characteristic 0, we define a moduli stack of principal ρ-sheaves that compactifies the stack of G-bundles on X. We apply the recent theory of \(\Theta\)-stratificacions to construct a moduli space of Gieseker semistable principal ρ-sheaves, which provides an intrinsic stack-theoretic construction of the moduli space of semistable principal bundles over higher dimensional varieties. An important outcome is the definition of a Gieseker-Harder-Narasimhan filtration for ρ sheaves, which induces a stratification of the stack by locally closed substacks and refines the previously known canonical slope parabolic reduction.