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Algebra Seminar

On the boundedness of \(n\)-folds of Kodaira dimension \(n-1\)

Stefano Filipazzi (UCLA)

Date & time: Wednesday, 16 September 2020 at 2:00PM - 3:00PM

Abstract. One of the main topics in the classification of algebraic varieties is boundedness. Loosely speaking, a set of varieties is called bounded if it can be parametrized by a scheme of finite type. In the literature, there is extensive work regarding the boundedness of varieties belonging to the three building blocks of the birational classificaiton of varieties: varieties of Fano type, Calabi--Yau type, and general type. Recently, work of Di Cerbo--Svaldi and Birkar introduced ideas to deduce boundedness statements for fibrations from boundedness results concerning these three classes of varieties. Following this philosophy, in this talk I will discuss some natural conditions for a set of n-folds of Kodaira dimension n-1 to be bounded.

Part of this talk is based on joint work with Roberto Svaldi.