Algebraic geometry of bubbling Kahler metrics
Abstract
We give an algebro-geometric or non-archimedean framework to study bubbling phenomena of Kahler metrics with Euclidean volume growth, after [DS17, Sun23, dBS23]. In particular, for any degenerating family to log terminal singularity, we algebraically construct a finite sequence of birational modifications of the family with milder degenerations, and compare with analytic bubbling constructions in loc.cit. We also provide approaches in terms of coordinates and valuations. Our discussion partially depends on the general framework of stability theory in our [Od24b] (arXiv:2406.02489) after [HL14, AHLH23].
Keywords
Cite
@article{arxiv.2406.14518,
title = {Algebraic geometry of bubbling Kahler metrics},
author = {Yuji Odaka},
journal= {arXiv preprint arXiv:2406.14518},
year = {2025}
}
Comments
v3: Just incorporated original subsection 2.3 and appendix A (of v2) to a different file arXiv:2406.02489 (v3). No other mathematical changes