Lines, Twisted Cubics on Cubic Fourfolds, and the Monodromy of the Voisin Map
| Autor: | Giovenzana, Franco, Giovenzana, Luca |
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| Rok vydání: | 2024 |
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| Druh dokumentu: | Working Paper |
| Popis: | 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. Comment: 18 pages, Macaulay2 code included as an ancillary file. Comments are welcome! |
| Databáze: | arXiv |
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