K-stability of relative flag varieties
Algebraic Geometry
2015-11-11 v2
Abstract
We generalise partial results about the Yau-Tian-Donaldson correspondence on ruled manifolds to bundles whose fibre is a classical flag variety. This is done using Chern class computations involving the combinatorics of Schur functors. The strongest results are obtained when working over a Riemann surface. Weaker partial results are obtained for adiabatic polarisations over a base of arbitrary dimension. We develop the notion of relative K-stability which embeds the idea of working over a base variety into the theory of K-stability. Natural constructions in filtered algebras equip the collection of test configuration with extra structures. We illustrate these constructions with several examples.
Keywords
Cite
@article{arxiv.1307.7638,
title = {K-stability of relative flag varieties},
author = {Anton Isopoussu},
journal= {arXiv preprint arXiv:1307.7638},
year = {2015}
}