New rational cubic fourfolds arising from Cremona transformations
Algebraic Geometry
2023-06-01 v2
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.
Keywords
Cite
@article{arxiv.2003.00366,
title = {New rational cubic fourfolds arising from Cremona transformations},
author = {Yu-Wei Fan and Kuan-Wen Lai},
journal= {arXiv preprint arXiv:2003.00366},
year = {2023}
}
Comments
41 pages. Final version, accepted by Algebraic Geometry