Constant scalar curvature and Kähler manifolds with nef canonical bundle

Abstract: Given a compact Kähler manifold it is a classical question, related to K-stability, whether it admits a Kähler metric of constant scalar curvature (cscK metric for short). In this talk we prove that there always exist cscK metrics on compact Kähler manifolds with nef canonical bundle, thus on all smooth minimal models, and also on the blowup of any such manifold. This confirms an expectation of Jian-Shi-Song and extends well-known results of Aubin and Yau to the nef case, giving a large new class of examples of cscK manifolds. The tools used are from the variational approach in Kähler geometry, and some related results on stability thresholds and Donaldson's J-equation are discussed along the way.

algebraic geometrycombinatorics

Audience: researchers in the topic

Online Nottingham algebraic geometry seminar

Series comments: Online geometry seminar, typically held on Thursday. This seminar takes place online via Microsoft Teams on the Nottingham University "Algebraic Geometry" team.

For recordings of past talks, copies of the speaker's slides, or to be added to the Team, please visit the seminar homepage at: kasprzyk.work/seminars/ag.html