Degenerations of elliptic quartics and K-moduli of Fano threefolds

@misc{cheltsov2026degenerations,
  title = {{Degenerations of elliptic quartics and K-moduli of Fano threefolds}},
  author = {Ivan Cheltsov and Anne-Sophie Kaloghiros and Robert Śmiech and Junyan Zhao},
  howpublished = {arXiv},
  year = {2026},
  month = aug,
  doi = {10.48550/arxiv.2608.30855},
  eprint = {2608.30855},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2608.30855},
}

TY  - UNPB
TI  - Degenerations of elliptic quartics and K-moduli of Fano threefolds
AU  - Ivan Cheltsov
AU  - Anne-Sophie Kaloghiros
AU  - Robert Śmiech
AU  - Junyan Zhao
PY  - 2026
DA  - 2026/08/31
PB  - arXiv
DO  - 10.48550/arxiv.2608.30855
UR  - https://arxiv.org/abs/2608.30855
AB  - We study the K-moduli space of Fano threefolds obtained by first blowing up ℙ^3 along an elliptic quartic curve C and then blowing up a fiber ℓ_p of the exceptional divisor E → C. We prove that this K-moduli space is isomorphic to a VGIT quotient parametrizing pairs (C,p), with linearization induced by the CM line bundle. In particular, we classify all K-(semi/poly)stable members of this deformation family. The main new ingredients in the proof include the geometry of the Hilbert scheme of elliptic quartic curves, deformation theory of Fano--K3 pairs, and optimal bounds on the local volumes of threefold singularities.
ER  -