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master doc.out
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\BOOKMARK [0][-]{chapter*.4}{Declaration}{}% 1
\BOOKMARK [0][-]{chapter*.5}{Copyright}{}% 2
\BOOKMARK [0][-]{chapter*.6}{Acknowledgements}{}% 3
\BOOKMARK [0][-]{chapter.1}{Introduction}{}% 4
\BOOKMARK [1][-]{section.1.1}{Content of the Thesis}{chapter.1}% 5
\BOOKMARK [0][-]{chapter.2}{Preliminaries}{}% 6
\BOOKMARK [1][-]{section.2.1}{K\344hler geometry}{chapter.2}% 7
\BOOKMARK [2][-]{subsection.2.1.1}{Basic definitions}{section.2.1}% 8
\BOOKMARK [2][-]{subsection.2.1.2}{Line bundles and Kodaira Embedding}{section.2.1}% 9
\BOOKMARK [2][-]{subsection.2.1.3}{Canonical metrics on K\344hler manifolds}{section.2.1}% 10
\BOOKMARK [1][-]{section.2.2}{Algebraic and symplectic tools}{chapter.2}% 11
\BOOKMARK [2][-]{subsection.2.2.1}{The algebraic torus}{section.2.2}% 12
\BOOKMARK [2][-]{subsection.2.2.2}{Linearizations}{section.2.2}% 13
\BOOKMARK [2][-]{subsection.2.2.3}{Hamiltonian actions and moment maps}{section.2.2}% 14
\BOOKMARK [2][-]{subsection.2.2.4}{Chow and GIT quotients}{section.2.2}% 15
\BOOKMARK [1][-]{section.2.3}{T-varieties}{chapter.2}% 16
\BOOKMARK [2][-]{subsection.2.3.1}{Toric varieties}{section.2.3}% 17
\BOOKMARK [2][-]{subsection.2.3.2}{Higher complexity T-varieties}{section.2.3}% 18
\BOOKMARK [2][-]{subsection.2.3.3}{f-divisors and divisorial polytopes}{section.2.3}% 19
\BOOKMARK [1][-]{section.2.4}{Equivariant K-stability}{chapter.2}% 20
\BOOKMARK [2][-]{subsection.2.4.1}{Twisted equivariant K-stability}{section.2.4}% 21
\BOOKMARK [2][-]{subsection.2.4.2}{K-stability of T-varieties}{section.2.4}% 22
\BOOKMARK [0][-]{chapter.3}{K\344hler-Ricci solitons on Fano threefolds}{}% 23
\BOOKMARK [1][-]{section.3.1}{The method of proof}{chapter.3}% 24
\BOOKMARK [1][-]{section.3.2}{Two examples in detail}{chapter.3}% 25
\BOOKMARK [1][-]{section.3.3}{Barvinok Integration}{chapter.3}% 26
\BOOKMARK [0][-]{chapter.4}{R\(X\) in complexity one}{}% 27
\BOOKMARK [1][-]{section.4.1}{A short digression into convex geometry}{chapter.4}% 28
\BOOKMARK [1][-]{section.4.2}{Proof of Theorem 4}{chapter.4}% 29
\BOOKMARK [2][-]{subsection.4.2.1}{Product Configurations}{section.4.2}% 30
\BOOKMARK [2][-]{subsection.4.2.2}{Non-Product Configurations}{section.4.2}% 31
\BOOKMARK [0][-]{chapter.5}{K\344hler-Einstein metrics in complexity two}{}% 32
\BOOKMARK [1][-]{section.5.1}{Chow quotient calculations}{chapter.5}% 33
\BOOKMARK [2][-]{subsection.5.1.1}{Bidegree \(a,b\) hypersurfaces}{section.5.1}% 34
\BOOKMARK [2][-]{subsection.5.1.2}{A wonderful compactification on the quadric}{section.5.1}% 35
\BOOKMARK [1][-]{section.5.2}{Log canonical thresholds and Tian's criterion}{chapter.5}% 36
\BOOKMARK [2][-]{subsection.5.2.1}{Log canonical thresholds}{section.5.2}% 37
\BOOKMARK [2][-]{subsection.5.2.2}{Tian's alpha invariant and criterion}{section.5.2}% 38
\BOOKMARK [2][-]{subsection.5.2.3}{Log canonical threshold bounds}{section.5.2}% 39
\BOOKMARK [0][-]{chapter.6}{Conclusions and further work}{}% 40
\BOOKMARK [0][-]{appendix.A}{Threefold Data}{}% 41
\BOOKMARK [0][-]{appendix.B}{SageMath Code}{}% 42
\BOOKMARK [0][-]{appendix*.50}{Bibliography}{}% 43