Lines, Twisted Cubics on Cubic Fourfolds, and the Monodromy of the Voisin Map

Abstract

For a general cubic fourfold $Y$ with associated Fano variety of lines $F$, we show that the monodromy group of the finite degree 16 rational Voisin self-map $\psi :F⇢F$ is maximal. To achieve this, we investigate the intriguing interplay between $\psi$ and the fixed locus of the antisymplectic involution on the LLSvS variety $Z$, examined via the degree 6 Voisin map $F\times F⇢Z$.

v1:18 pages, Macaulay2 code included as an ancillary file. v2: Minor changes. v3:final version to appear on EPIGA. Comments are welcome!