Seminar Algebra and Geometry: Francesco Denisi (Université Paris-Cité)

On the birational geometry of some hypersurfaces

Mori dream spaces form a class of algebraic varieties that play a significant role in birational geometry, as they exhibit ideal behaviour within the minimal model program. In this talk, we first motivate and discuss the notion of a Mori dream space, providing numerous examples and non-examples. We then explore the birational geometry of hypersurfaces in products of weighted projective spaces, as well as in more general ambient spaces, focusing in particular on cases where such hypersurfaces are Mori dream spaces. We generalise results previously obtained by J.C. Ottem and, if time permits, conclude with a few remarks on the Kawamata–Morrison cone conjecture for certain anticanonical Calabi–Yau hypersurfaces in products of weighted projective spaces.

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