Seminar| Institute of Mathematical Sciences
Time:Thursday, June 5th, 2025, 09:00-10:00
Location:IMS, RS408
Speaker:Mingchen Xia, Institute of Geometry and Physics, USTC
Abstract:In toric geometry, it is known that the geometric properties of a toric line bundle are closely related to a convex polytope, known as the Newton polytope. Based on the work of Okounkov, Lazarsfeld--Mustață and Kaveh—Khovanskii extended the Newton polytope to big line bundles on general projective manifolds.
In the thesis of Ya Deng, the construction was extended to general transcendental big cohomology classes on compact Kähler manifolds as well. It remains unclear if the transcendental Okounkov bodies have the expected volume. In this talk, we will confirm this and hence answering a conjecture of Lazarsfeld--Mustață, Demailly and Deng. Joint work with Kewei Zhang, Tamás Darvas, David Witt Nyström and Rémi Reboulet.