New rational cubic fourfolds arising from Cremona transformations

2020/02/29 by Fan, Yu-Wei, Lai, Kuan-Wen · 3 citations
#Algebraic Geometry (math.AG) #FOS: Mathematics

paper · doi:10.48550/arxiv.2003.00366

Abstract

Are Fourier-Mukai equivalent cubic fourfolds birationally equivalent? We obtain an affirmative answer to this question for very general cubic fourfolds of discriminant 20, where we produce birational maps via the Cremona transformation defined by the Veronese surface. By studying how these maps act on the cubics known to be rational, we surprisingly found new rational examples.

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• L-equivalence and Fourier--Mukai partners of cubic fourfolds
• Some remarks on L-equivalence for cubic fourfolds and hyper-Kähler manifolds
• Counting Fourier-Mukai partners of cubic fourfolds

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