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 $\psi \colon F \dashrightarrow F$ 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 \dashrightarrow Z $.