Normal stable degenerations of Noether-Horikawa surfaces

Hiroto Akaike; Makoto Enokizono; Masafumi Hattori; Yuki Koto

Normal stable degenerations of Noether-Horikawa surfaces

Algebraic Geometry 2025-07-24 v1 Differential Geometry Geometric Topology

Authors: Hiroto Akaike , Makoto Enokizono , Masafumi Hattori , Yuki Koto

Abstract

We classify all normal stable Horikawa surfaces with only $\mathbb{Q}$ -Gorenstein smoothable log canonical singularities. Furthermore, we provide a criterion for their global $\mathbb{Q}$ -Gorenstein smoothability and describe the boundary strata of the moduli space of $\mathbb{Q}$ -Gorenstein smoothable normal stable Horikawa surfaces.

Keywords

Noether-Horikawa surfaces stable degenerations Q-Gorenstein smoothability moduli space log canonical singularities

Cite

@article{arxiv.2507.17633,
  title  = {Normal stable degenerations of Noether-Horikawa surfaces},
  author = {Hiroto Akaike and Makoto Enokizono and Masafumi Hattori and Yuki Koto},
  journal= {arXiv preprint arXiv:2507.17633},
  year   = {2025}
}

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218 pages. Comments are welcome!

Normal stable degenerations of Noether-Horikawa surfaces

Abstract

Keywords

Cite

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