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Title: Stability of varieties with a torus action
Author: Cable, Jacob
ISNI:       0000 0004 9352 3248
Awarding Body: University of Manchester
Current Institution: University of Manchester
Date of Award: 2020
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In this thesis we study several problems related to the existence problem of invariant canonical metrics on Fano manifolds in the presence of an effective algebraic torus action. The first chapter gives an introduction. The second chapter reviews the existing theory of T-varieties and reviews various stability thresholds and K-stability constructions which we make use of to obtain new results. In the third chapter we discuss some joint work with my supervisor to find new Kähler-Ricci solitons on smooth Fano threefolds admitting a complexity one torus action. In the fourth chapter we present a new formula for the greatest lower bound on Ricci curvature, an invariant which is now known to coincide with Tian's delta invariant. In the fifth chapter we find new Kähler-Einstein metrics on some general arrangement varieties.
Supervisor: Borovik, Alexandre ; Suess, Hendrik Sponsor: Not available
Qualification Name: Thesis (Ph.D.) Qualification Level: Doctoral
EThOS ID:  DOI: Not available
Keywords: complexity one ; alpha invariant ; complex geometry ; algebraic geometry ; KA~¤hler-Einstein metrics ; KA~¤hler-Ricci solitons ; K-stability