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

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 ψ F F is maximal. To achieve this, we investigate the intriguing interplay between $ ψ$ and the fixed locus of the antisymplectic involution on the LLSvS variety Z, examined via the degree 6 Voisin map F × 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!