Foldable fans, cscK surfaces and local K-moduli
Algebraic Geometry
2025-10-01 v2 Differential Geometry
Abstract
We study the moduli space of constant scalar curvature K\"ahler surfaces around the toric ones. To this aim, we introduce the class of foldable surfaces : smooth toric surfaces whose lattice automorphism group contain a non trivial cyclic subgroup. We classify such surfaces and show that they all admit a constant scalar curvature K\"ahler metric (cscK metric). We then study the moduli space of polarised cscK surfaces around a point given by a foldable surface, and show that it is locally modeled on a finite quotient of a toric affine variety with terminal singularities.
Cite
@article{arxiv.2402.01159,
title = {Foldable fans, cscK surfaces and local K-moduli},
author = {Carl Tipler},
journal= {arXiv preprint arXiv:2402.01159},
year = {2025}
}
Comments
Expanded version, and minor corrections. 28 pages, 13 figures. To appear in Moduli - Foundation Compositio Mathematica