K-semistability of optimal degenerations

Dervan, R. (2020) K-semistability of optimal degenerations. Quarterly Journal of Mathematics, 71(3), pp. 989-995. (doi: 10.1093/qmathj/haaa012)

Abstract

K-polystability of a polarized variety is an algebro-geometric notion conjecturally equivalent to the existence of a constant scalar curvature Kähler metric. When a variety is K-unstable, it is expected to admit a ‘most destabilizing’ degeneration. In this note we show that if such a degeneration exists, then the limiting scheme is itself relatively K-semistable.

• Item Type: Articles
• Status: Published
• Refereed: Yes
• Glasgow Author(s) Enlighten ID: Dervan, Dr Ruadhaí
• Authors: Dervan, R.
• College/School: College of Science and Engineering > School of Mathematics and Statistics > Mathematics
• Journal Name: Quarterly Journal of Mathematics
• Publisher: Oxford University Press
• ISSN: 0033-5606
• ISSN (Online): 1464-3847
• Published Online: 15 July 2020
• Copyright Holders: Copyright © The Author(s) 2020
• First Published: First published in The Quarterly Journal of Mathematics 71(3):989–995
• Publisher Policy: Reproduced in accordance with the publisher copyright policy