Triangle varieties and surface decomposition of hyper-Kahler manifolds

Abstract: In recent years, new constructions of complete families of polarized hyper-Kahler manifolds have been found starting from Fano geometry. These hyper-Kahler manifolds also appear as general deformations of Hilbert schemes of K3 surfaces or O'Grady manifolds. I will introduce the notion of surface decomposition for a variety X with a nontrivial Hodge structure on degree 2 cohomology. I will show that this notion is restrictive topologically, as it implies Beauville-Fujiki type relations. I will also show the existence of such a surface decomposition for the general hyper-Kahler manifolds mentioned above. This has interesting consequences on Beauville's conjecture on the Chow ring of hyper-Kahler manifolds.

algebraic geometry

Audience: researchers in the topic

ZAG (Zoom Algebraic Geometry) seminar

Series comments: Description: ZAG seminar

The seminar takes place on Tuesdays and Thursdays via Zoom. Zoom passwords are given via mailing list on Fridays. To join the mailing list go to the website.

If you use a calendar system, you can see the individual seminars at bit.ly/zag-seminar-calendar

Times vary to accommodate speakers time zones but times will be announced in GMT time.