Curve classes on conic bundle threefolds and applications to rationality
Algebraic Geometry and Number Theory Seminar
Date
Thursday, January 25, 2024 13:00 - 15:00
Speaker
Soumya Sankar (Utrecht University)
Location
Heinzel Seminar Room (I21.EG.101), Office Building West, ISTA
Series
Seminar/Talk
Tags
Mathematics and CS Seminar, mathematical_seminar_ics
Host
Tim Browning
Contact
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 describe curve classes on certain conic bundle threefolds over arbitrary fields in terms of rational points on certain torsors of a Prym variety. We then use the description of these classes to study the rationality of such threefolds.