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Title:
Some new rational cubic 4-folds
Speaker:
Abstract:
I will begin by recalling the beautiful story of cubic 4-folds containing a plane: the quadric surface fibration over P2, the K3 surface of degree 2 with the Brauer class of order 2, the countable union of 18-dimensional families of rational cubics, etc. Then I will discuss some new work, joint with Hassett, Tschinkel, and Várilly-Alvarado, which yields a similar story for cubics containing an elliptic ruled surface: there is a sextic del Pezzo fibration over P2, and a K3 surface of degree 2 with a Brauer class of order 3, and a countable union of 18-dimensional families of rational cubics. These are the first new rational cubic 4-folds to come along in in two decades.
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