On the (uni)rationality problem for quadric bundles and hypersurfaces

Abstract: A variety $X$ over a field is unirational if there is a dominant rational map from a projective space to $X$. We will discuss the unirationality problem for quartic hypersurfaces and quadric bundles over a arbitrary field in the the perspective of the relation between unirationality and rational connectedness. We will prove unirationality of quadric bundles under certain positivity assumptions on their anti-canonical divisor. As a consequence we will get the unirationality of any smooth 4-fold quadric bundle over the projective plane, over an algebraically closed field, and with discriminant of degree at most 12.

algebraic geometrycombinatorics

Audience: researchers in the topic

Online Nottingham algebraic geometry seminar

Series comments: Online geometry seminar, typically held on Thursday. This seminar takes place online via Microsoft Teams on the Nottingham University "Algebraic Geometry" team.

For recordings of past talks, copies of the speaker's slides, or to be added to the Team, please visit the seminar homepage at: kasprzyk.work/seminars/ag.html