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Delta-invariants of Fano Varieties

Student: Golota Aleksei

Supervisor: Konstantin Shramov

Faculty: Faculty of Mathematics

Educational Programme: Mathematics (Master)

Final Grade: 10

Year of Graduation: 2019

For a polarized variety $(X, L)$ and a closed subgroup $G \subset \aut(X, L)$ we define a $G$-invariant version of the $\delta$-threshold. We prove that for a Fano variety $(X, -K_X)$ and a connected subgroup $G \subset \aut(X)$ this invariant characterizes $G$-equivariant $K$-stability. We also use this invariant to investigate $G$-equivariant $K$-stability of some Fano varieties with large groups of symmetries, including spherical Fano varieties.

Full text (added May 31, 2019)

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