Kahler-Ricci flow on rational homogeneous varieties

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Author(s):	Correa, Eder M. Total Authors: 1
Document type:	Journal article
Source:	Journal of Algebra; v. 629, p. 38-pg., 2023-09-01.
Abstract
In this work, we study the Kahler-Ricci flow on rational homo-geneous varieties exploring the interplay between projective algebraic geometry and representation theory which underlies the classical Borel-Weil theorem. By using elements of repre-sentation theory of semisimple Lie groups and Lie algebras, we give an explicit description for all solutions of the Kahler-Ricci flow with homogeneous initial condition. This description en-ables us to compute explicitly the maximal existence time for any solution starting at a homogeneous Kahler metric and obtain explicit upper and lower bounds for several geometric quantities along the flow, including curvatures, volume, diam-eter, and the first non-zero eigenvalue of the Laplacian. As an application of our main result, we investigate the relationship between certain numerical invariants associated with ample divisors and numerical invariants arising from solutions of the Kahler-Ricci flow in the homogeneous setting. (c) 2023 Elsevier Inc. All rights reserved. (AU)

FAPESP's process:	22/10429-3 - Hermitian geometry with torsion on principal bundles and applications
Grantee:	Eder de Moraes Correa
Support Opportunities:	Regular Research Grants