The role of automorphisms in the classification of surfaces of general type in characteristic $p>0$.

Nikolaos Tziolas (University of Cyprus)

14-Mar-2022, 14:00-15:00 (2 years ago)

Abstract: The classification of varieties of general type is one of the fundamental problems of algebraic geometry. In characteristic zero it is known that varieties of general type with fixed volume have a coarse moduli space of finite type over the base field and the corresponding moduli stack is Deligne-Mumford. In positive characteristic the first property is at the moment unknown if it holds in dimensions at least $3$ and the second fails in general in dimension at least $2$.

In this talk I will explain how the failure of the second property is related to the existence of varieties of general type with non reduced automorphism scheme. I will present explicit examples of such surfaces and present results regarding their geometry and the structure of their automorphism scheme.

Mathematics

Audience: researchers in the topic


Greek Algebra & Number Theory Seminar

Organizers: Dimitrios Chatzakos*, Maria Chlouveraki, Ioannis Dokas, Angelos Koutsianas*, Chrysostomos Psaroudakis
*contact for this listing

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