### Ivan Cheltsov

University of Edinburgh

Thursday 25 January 2024, 4.00pm – 5.00pm

Lecture Theatre D (Mathematical Institute)

** When a cubic 3-fold is equivariantly rational? **

A classical theorem of Clemens and Griffiths says that a smooth cubic 3-fold is irrational, i.e. it does not admit (generically one-to-one) rational parametrization. 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 a three-dimensional (projective) space? I will try to answer this question (but I will not answer it completely).

series: Pure Mathematics Colloquium

organiser: Scott Harper