Expanded degenerations for Hilbert schemes of points

  • Calla Tschanz

Student thesis: Doctoral ThesisPhD

Abstract

The aim of this thesis is to extend the expanded degeneration construction of Li and Wu to obtain good degenerations of Hilbert schemes of points on semistable families of surfaces, as well as to discuss alternative stability conditions and parallels to the GIT construction of Gulbrandsen, Halle and Hulek and logarithmic Hilbert scheme constructions of Maulik and Ranganathan. We construct some good degenerations of Hilbert schemes of points as proper Deligne- Mumford stacks and show that these provide geometrically meaningful examples of constructions arising from the work of Maulik and Ranganathan.
Date of Award13 Sept 2023
Original languageEnglish
Awarding Institution
  • University of Bath
SupervisorFran Burstall (Supervisor) & Gregory Sankaran (Supervisor)

Keywords

  • algebraic geometry

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