Speaker: Olivier Benoist

Time: 10:00-12:00am, April 1st, 3rd, 8th, 10th and 15th. 2015

Venue: Room 82J04, Jiayibing Building,BICMR

Abstract : Decomposition of the diagonal is a technique introduced in the 80s by Bloch and Srinivas to study the interplay between geometry and cohomology of algebraic varieties. In a recent series of papers, Voisin has started to investigate integrality properties of decompositions of the diagonal.

As an application, she gave new examples of rationally connected varieties that are not stably rational. This strategy has been developped and applied to many more examples by Colliot-Thélène/Pirutka, Beauville and Totaro.

Another application of her work is the first example of a rationally connected threefold whose Abel-Jacobi map for 1-cycles is not induced by a universal family.

In this lecture, after recalling classical results, we will explain Voisin's work with an emphasis on the two applications described above.