Geometry Seminar
The moduli stack of principal ρ-sheaves and Gieseker-Harder-Narasimhan filtrations
Speaker: Alfonso Zamora (UPM)Date: Wednesday, 01 June 2022 - 15:30Place: 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.