When a cubic 3-fold is equivariantly rational?
Ivan Cheltsov (Edinburgh)
A classical theorem of Clemens and Griffiths says that a smooth cubic 3-fold is irrational, i.e. it does not admit any birational map to the three-dimensional projective space. On the other hand, every singular cubic 3-fold is rational (unless it is a cone over a smooth cubic curve). Since many singular cubic 3-folds have symmetries, it is natural to ask when a singular cubic 3-fold (acted on by a finite group G) is G-equivariantly rational? That is to say, when does it admit a G-equivariant birational map to the three-dimensional projective space? In my talk, I will try to answer this question.
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