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Peer-reviewedCC BY 4.0Moduli

Foldable fans, cscK surfaces and local K-moduli

  • Carl Tipler
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Abstract

We study the moduli space of constant scalar curvature Kähler (cscK) surfaces around toric surfaces. To this end, we introduce the class of foldable surfaces: smooth toric surfaces whose lattice automorphism group contains a non-trivial cyclic subgroup. We classify such surfaces and show that they all admit a 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 modelled on a finite quotient of a toric affine variety with terminal singularities.

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Cite

BibTeXRIS
BibTeX
@article{tipler2026foldable,
  title = {{Foldable fans, cscK surfaces and local K-moduli}},
  author = {Carl Tipler},
  journal = {Moduli},
  year = {2026},
  month = sep,
  doi = {10.1112/mod.2025.10005},
  url = {https://hal.science/hal-05738402v1},
  note = {CC BY 4.0},
}
RIS
TY  - JOUR
TI  - Foldable fans, cscK surfaces and local K-moduli
AU  - Carl Tipler
PY  - 2026
DA  - 2026/09/04
JO  - Moduli
DO  - 10.1112/mod.2025.10005
UR  - https://hal.science/hal-05738402v1
AB  - We study the moduli space of constant scalar curvature Kähler (cscK) surfaces around toric surfaces. To this end, we introduce the class of foldable surfaces: smooth toric surfaces whose lattice automorphism group contains a non-trivial cyclic subgroup. We classify such surfaces and show that they all admit a 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 modelled on a finite quotient of a toric affine variety with terminal singularities.
SN  - 2949-7647
ER  -