Seminar Algebra and Geometry: Daniela Paiva (IMPA)

Birational geometry of Fano 3-folds and anticanonical surfaces

The problem of determining which automorphisms of a projective K3 surface S are induced by birational maps of an ambient space in which it is embedded remains open. This is known as Gizatullin’s problem.
In this seminar, I will provide a general background on the theory of K3 surfaces and the birational geometry of Fano 3-folds, and explain how the interplay between these areas can be exploited to address the problem. In particular, I will present a solution to Gizatullin’s problem in certain specific cases.
The results I will present are part of joint work with Carolina Araujo, Michela Artebani, Alice Garbagnati, Ana Quedo, and Sokratis Zikas.

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