Tautological differential forms on moduli spaces of curves

Lugt, S. van der (2022)

Doctoral Thesis

In this thesis we study the moduli space of genus g curves, and the differential forms that occur naturally on this moduli space. We show that the rings of these tautological differential forms are finite-dimensional, and discuss algorithms that can be used to compute relations among tautological differential forms.

• Algebraic geometry
• Complex geometry
• Moduli spaces
• Stacks
• Tautological ring
• Tautological differential forms

• All authors: Lugt, S. van der
• Supervisor: Luijk, R.M. van; Edixhoven, S.J.
• Co-supervisor: Jong, R.S. de
• Committee: Faber, C.F.; Holmes, D.S.T.; Petersen, D.; Spieksma, F.M.
• Qualification: Doctor (dr.)
• Awarding Institution: Mathematical Institute (MI), Faculty of Science, Leiden University
• Date: 2022-04-12
• Sponsorship: The research for this thesis was financed by TOP grant 613.001.401 "Refined tautological relations on moduli spaces of curves" of the Dutch Research Council (NWO)