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arXiv · 2107.14319

Equivariant geometry of odd-dimensional complete intersections of two quadrics

Brendan Hassett·Yuri Tschinkel
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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.

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Brendan Hassett, Yuri Tschinkel. 2021-07-29. Equivariant geometry of odd-dimensional complete intersections of two quadrics. https://arxiv.org/abs/2107.14319

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