Abstract: A variety is retract rational if the solutions of its defining equation can be parametrized by rational functions. Examples are provided by rational or stably rational varieties. We explain some history on the problem of deciding whether a given variety is (retract) rational, concentrating mostly on the case of cubics. We will then explain how recent joint work with Engel and de Gaay Fortman on the failure of the integral Hodge conjecture for abelian varieties implies by earlier work of Voisin that very general cubic threefolds over the field of complex numbers are not retract rational, hence not stably rational.
Il seminario si svolgerà in presenza nell'aula M1. Per ulteriori informazioni, si può contattare gli organizzatori all'email amos.turchet@uniroma3.it.
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