Rationality of Fano threefolds over non-closed fields

2019/11/20 by Kuznetsov, Alexander, Prokhorov, Yuri · 5 citations
#14E08 #14E30 #Algebraic Geometry (math.AG) #FOS: Mathematics

paper · doi:10.48550/arxiv.1911.08949

Abstract

We give necessary and sufficient conditions for unirationality and rationality of Fano threefolds of geometric Picard rank-1 over an arbitrary field of zero characteristic.

Cited by

• Fano threefolds
• Degree two unirational parametrizations over the real field
• Equivariant rationality of Fano threefolds in the family \textnumero 2.12
• A rationality criterion for real Fano threefolds
• Smooth Fano 3-folds satisfying Condition (A)

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• Rationality of Fano threefolds of degree 18 over nonclosed fields
• A rationality criterion for real Fano threefolds
• Rational points on log Fano threefolds over a finite field
• Fano threefolds in positive characteristic III