Higher complex structures
Differential Geometry
2025-07-08 v4 Mathematical Physics
math.MP
Abstract
We introduce and analyze a new geometric structure on topological surfaces generalizing the complex structure. To define this so called higher complex structure we use the punctual Hilbert scheme of the plane. The moduli space of higher complex structures is defined and is shown to be a generalization of the classical Teichm\"uller space. We give arguments for the conjectural isomorphism between the moduli space of higher complex structures and Hitchin's component.
Cite
@article{arxiv.1812.11199,
title = {Higher complex structures},
author = {Vladimir V. Fock and Alexander Thomas},
journal= {arXiv preprint arXiv:1812.11199},
year = {2025}
}
Comments
15 pages