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
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.
Engineering and Physical Sciences Research Council (EP/N01815X/1)
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