Abstract: On a compact Kähler manifolds, (1,1) classes which are on the boundary of the Kähler cone and have positive volume are not far from being Kähler, in the sense that they contain a Kähler current with analytic singularities (this follows from a fundamental result of Demailly-Paun). This can be thought of as a Kähler metric with some singularities along an analytic subset, and the smallest such subset is called the non-Kähler locus of the class. I will discuss a geometric characterization of the non-Kähler locus in terms of subvarieties which have trivial intersection with the class. I will also mention some applications of this result, including a solution of a conjecture of Feldman-Ilmanen-Knopf and Campana which says that finite-time singularities of the Kähler-Ricci flow form along analytic subvarieties, as well as an application to degenerations of Ricci-flat Calabi-Yau manifolds. This is joint work with Tristan Collins.

Time: 10:10am-12:00pm, Friday, June 12.

Place: Room 29, Quan Zhai, BICMR

Speaker:Valentino Tosatti, Northwestern University