Generators of Derived Category and Toric Frobenius Morphism

Student: Dosaev Rinat

Supervisor: Aleksandr Kuznetsov

Educational Programme: Mathematics (Master)

Year of Graduation: 2024

We investigate the behavior of toric Frobenius pushforward applied to line bundles on smooth toric varieties. The main question for us is for which line bundles we obtain the generator of derived category in this way. There is a conjecture of A.Hanlon, J.Hicks and O.Lazarev which characterizes such line bundles in terms of some special toric subvarieties. We prove this conjecture for the projectivization of a split vector bundle on a smooth toric variety for which a slightly stronger version of conjecture is known.

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