Equivariant geometry of odd-dimensional complete intersections of two quadrics

Abstract

Fix a finite group $G$. We seek to classify varieties with $G$-action equivariantly birational to a representation of $G$ on affine or projective space. Our focus is odd-dimensional smooth complete intersections of two quadrics, relating the equivariant rationality problem with analogous Diophantine questions over nonclosed fields. We explore how invariants -- both classical cohomological invariants and recent symbol constructions -- control rationality in some cases.

31 pages

References in corpus (6)

• Intermediate Jacobians and rationality over arbitrary fields
• Equivariant birational types and Burnside volume
• Cycle class maps and birational invariants
• Rationality of complete intersections of two quadrics
• Symbols and equivariant birational geometry in small dimensions
• The geometry of antisymplectic involutions, I