K-moduli of log del Pezzo pairs and variations of GIT
Algebraic Geometry
2024-07-01 v1
Abstract
We study the K-moduli of log del Pezzo pairs formed by a del Pezzo surface of degree and an anti-canonical divisor. These moduli spaces naturally depend on one parameter, providing a natural problem in variations of K-moduli spaces. For degrees 2, 3, 4, we establish an isomorphism between the K-moduli spaces and variations of Geometric Invariant Theory compactifications, which generalizes the isomorphisms in the absolute cases established by Odaka--Spotti--Sun and Mabuchi--Mukai.
Cite
@article{arxiv.2406.20008,
title = {K-moduli of log del Pezzo pairs and variations of GIT},
author = {Jesus Martinez-Garcia and Theodoros Stylianos Papazachariou and Junyan Zhao},
journal= {arXiv preprint arXiv:2406.20008},
year = {2024}
}
Comments
41 pages, 6 tables. Comments are very welcome!