Stefano Filipazzi (Duke)
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PDL C-38
Title: On the classification of algebraic varieties
Abstract: The Minimal Model Program (MMP) is a powerful tool that helps understanding varieties up to birational equivalence. In particular, the MMP helps to identify three fundamental classes of varieties: Fano varieties, K-torsion varieties, and canonical models. In this talk, I will sketch how the MMP works and discuss the main properties of these classes of varieties, with special focus on K-torsion varieties.
Title: On the boundedness of fibered K-trivial varieties
Abstract: A K-trivial variety X is a normal projective variety with mild singularities whose canonical divisor K_X is linearly trivial. Examples of K-trivial varieties include abelian varieties, Calabi-Yau varieties, and hyperkähler varieties. In dimension 2, a K-trivial surface is either a (singular) K3 surface or an abelian surface. Starting with dimension 3, there is no complete classification of K-trivial varieties. In this talk, I will discuss recent progress about the classification of K-trivial varieties that admit a fibration. This talk is based on joint work with P. Engel, F. Greer, M. Mauri, and R. Svaldi.