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Equivariant geometry of odd-dimensional complete intersections of two quadrics
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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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Equivariant rationality of Fano threefolds in the family \textnumero 2.12
A faithful group action on a smooth complete intersection of three (1,1) divisors in P^3 x P^3 is linearizable exactly when the group does not mix the two projections, i.e., when the equivariant Picard group has rank 2.
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