标题： 直线，三次四维体上的扭曲三次曲线，以及Voisin映射的单值群 显示英文标题

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

摘要： 对于一个三次四维空间$ Y $和其关联的线的Fano流形$ F $，我们建立了由Voisin引入的有限次数16自有理映射$ \psi \colon F \dashrightarrow F $的几个性质。 我们首先分析在特殊化到$ \psi $的分支点集中的直线时，与一般直线相关的具有16个节点的节点五次曲面的奇点。 这种方法揭示了$ \psi $的不定性自然解析的分歧是简单的。 The main part of the paper focuses on 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 $. As an application, we show that the monodromy of $ \psi $ is maximal. 显示英文摘要

摘要： For a cubic fourfold $ Y $ with associated Fano variety of lines $ F $, we establish several properties of the finite-degree 16 self-rational map $ \psi \colon F \dashrightarrow F $ introduced by Voisin. We begin by analyzing the singularities of the nodal quintic with 16 nodes associated with a general line under the specialization to a line in the branch locus of $ \psi $. This approach reveals that the ramification of the natural resolution of indeterminacy of $ \psi $ is simple. The main part of the paper focuses on 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 $. As an application, we show that the monodromy of $ \psi $ is maximal.