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Log Calabi-Yau wall crossing for moduli of cubic surfaces

  • Hanfeng Chu
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Abstract

We study the wall crossing for the moduli space of unmarked cubic surfaces at the log Calabi-Yau threshold. We prove the existence of a good moduli space for the corresponding moduli stack of boundary polarized Calabi-Yau pairs with Gorenstein underlying surfaces and describe the wall crossing morphisms explicitly. More precisely, the morphism from the K-moduli space to the log Calabi-Yau moduli space is an isomorphism, whereas the morphism from the KSBA moduli space contracts a divisor isomorphic to ℙ3 to a point and is an isomorphism away from this divisor.

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Cite

BibTeXRIS
BibTeX
@misc{chu2026calabiyau,
  title = {{Log Calabi-Yau wall crossing for moduli of cubic surfaces}},
  author = {Hanfeng Chu},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.34429},
  eprint = {2609.34429},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.34429},
}
RIS
TY  - UNPB
TI  - Log Calabi-Yau wall crossing for moduli of cubic surfaces
AU  - Hanfeng Chu
PY  - 2026
DA  - 2026/09/28
PB  - arXiv
DO  - 10.48550/arxiv.2609.34429
UR  - https://arxiv.org/abs/2609.34429
AB  - We study the wall crossing for the moduli space of unmarked cubic surfaces at the log Calabi-Yau threshold. We prove the existence of a good moduli space for the corresponding moduli stack of boundary polarized Calabi-Yau pairs with Gorenstein underlying surfaces and describe the wall crossing morphisms explicitly. More precisely, the morphism from the K-moduli space to the log Calabi-Yau moduli space is an isomorphism, whereas the morphism from the KSBA moduli space contracts a divisor isomorphic to ℙ^3 to a point and is an isomorphism away from this divisor.
ER  -