Asymptotic Chow Stability on Symmetric Reflexive Toric Varieties
Ponente: King Leung Lee (ICMAT)Fecha: miércoles 15 de marzo de 2023 - 11:30Lugar: Aula Gris 3, ICMAT
In [-, Li, Sturm, Wang (2019)], using a result of Futaki and Ono, we checked the Chow stability of various toric surfaces. It can be checked that indeed all symmetric reflexive toric surfaces are asymptotic Chow polystable. We also provide examples of a symmetric, but non-reflexive toric surface that is not stable, and an example of a non-symmetric toric surface that is not stable. So it is natural to ask if a symmetric reflexive toric variety is asymptotic Chow polystable. The answer is no. However, if adding some conditions, then it is asymptotic Chow polystable.
In this talk, I will first recall the definition of asymptotic Chow stability, and state the result from Futaki and Ono that when a polarized toric variety is asymptotic Chow polystable. After that, I will provide an example of a non-stable symmetric reflexive toric variety. Then I will give a sufficient condition, which is called special, that a symmetric reflexive toric variety is polystable, and provide a sketch proof. Then I will provide examples of special varieties. If time is allowed, I will provide other criteria.