Irrationality and monodromy for cubic threefolds
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Authors
Smith, Ivan
Publication Date
2022-02-14Journal Title
ANNALI SCUOLA NORMALE SUPERIORE - CLASSE DI SCIENZE
ISSN
0391-173X
Publisher
Scuola Normale Superiore - Edizioni della Normale
Pages
24-24
Type
Article
This Version
AM
Metadata
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Smith, I. (2022). Irrationality and monodromy for cubic threefolds. ANNALI SCUOLA NORMALE SUPERIORE - CLASSE DI SCIENZE, 24-24. https://doi.org/10.2422/2036-2145.202005_006
Abstract
Let M denote the moduli space of smooth cubic threefolds. We prove that the monodromy 1(M) ! Sp(10;Z) of the 3rd cohomology groups on the fibres of the universal family does not factor through the genus five mapping class group. This gives a geometric group theory perspective on the well-known irrationality of cubic threefolds, and provides evidence for a corresponding symplectic nonrationality conjecture.
Sponsorship
Engineering and Physical Sciences Research Council (EP/N01815X/1)
Identifiers
External DOI: https://doi.org/10.2422/2036-2145.202005_006
This record's URL: https://www.repository.cam.ac.uk/handle/1810/334913
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