241012 Soumya Sankar

October 24, 2023

Title: Curve classes on conic bundle threefolds and applications to rationality (MI talk)

Speaker: Soumya Sankar

A variety is called rational if it admits a birational map to projective space. One of the major programs in algebraic geometry seeks to understand when a given variety is rational, and what the obstructions to rationality are. From this perspective, conic bundles are a geometrically rich class of varieties. I will talk about joint work with Sarah Frei, Lena Ji, Bianca Viray and Isabel Vogt, where we study curve classes on certain conic bundle threefolds over arbitrary fields of odd characteristic. We then use the description of these classes to study the rationality of such varieties.

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