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

2024/12/10 by Franco Giovenzana, Giovenzana, Franco, Luca Giovenzana +1 · 1 citation
Mathematics · #Mathematics and Applications #Advanced Differential Equations and Dynamical Systems #Geometric and Algebraic Topology

paper · pdf · doi:10.48550/arxiv.2412.07483

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 ψ\colon F \dashrightarrow 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 \dashrightarrow Z .

Cited by

• Galois covers of Calabi-Yau manifolds

Related

• The Fermat cubic and monodromy of lines
• On the uniruled Voisin divisor on the LLSvS variety
• The Voisin map via families of extensions
• Twisted cubics on cubic fourfolds and stability conditions
• Algebraic cycles and very special cubic fourfolds