Normal stable degenerations of Noether-Horikawa surfaces

Q: What type of study is this?

This is a Quantitative Study study.

Hiroto Akaike; Makoto Enokizono; Masafumi Hattori; Yuki Koto

doi:10.48550/arxiv.2507.17633

July 23, 2025Open Access

Normal stable degenerations of Noether-Horikawa surfaces

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Key Points

Normal stable Horikawa surfaces are classified based on their singularities, providing a clear structure within the moduli space.
A criterion for $ ext{Q}$-Gorenstein smoothability is established, allowing for better understanding of these surfaces.
The study highlights the boundary strata of the moduli space, offering vital insights into the structure of these surfaces.
Insights into log canonical singularities are provided, which are crucial for understanding the geometry of these surfaces.

Implication

This paper classifies normal stable Horikawa surfaces with log canonical singularities, indicating their smoothability characteristics.

Abstract

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

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Cite This Study

Akaike et al. (2025) studied this question.

synapsesocial.com/papers/68e6a0f4718ef0a556b33e61 https://doi.org/10.48550/arxiv.2507.17633

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Normal stable degenerations of Noether-Horikawa surfaces

Key Points

Implication

Abstract

Discussion

Cite This Study

Normal stable degenerations of Noether-Horikawa surfaces

Key Points

Implication

Abstract

Discussion

Cite This Study

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