Group actions and stability notions on algebraic varieties

Abstract

In this thesis, we investigate the stability of the tangent bundles of various types of algebraic surfaces. We begin by introducing the notion of slope stability in the sense of Mumford and Takemoto and review some preliminaries concerning the tools and techniques we employ to prove later results. We generalise a result by Hering-Nils-Suess concerning toric varieties to the case of complexity one C*-surfaces with fibrewise group actions. Next, we derive a criterion for the semistability of the tangent bundle of blow ups of Hirzebruch surfaces in the general setting and explore some examples and counterexamples. Finally, we give a full description or the tangent bundles of smooth Weierstrass fibrations using the topological Euler characteristic and the genus of the base curve.

Date of Award	10 Sept 2023
Original language	English
Awarding Institution	The University of Manchester
Supervisor	Hendrik Süß (Main Supervisor) & Christopher Frei (Co Supervisor)