Year: 2026
Type: preprint
Abstract: We describe a Cremona transformation on $\mathbb{P}^5$ given by the linear system of quintics that are double along the Fano model of an Enriques surface $S$. Using this Cremona transform, we construct a birational equivalence between the very general cubic fourfold $X$ of discriminant 44 and its unique Fourier--Mukai partner. We also classify birational maps between smooth, non-isomorphic cubic fourfolds resolved by blowing up a smooth surface on each side: the centres must be either Fano models of Enriques surfaces, as in our construction, or Veronese surfaces, as studied by Fan--Lai.
Source: arXiv (Cornell University)
Authors: Brooke, Corey, Marquand, Lisa
Institutions: St. Olaf College, Rutgers, The State University of New Jersey
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7212117428