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代数幾何学セミナー
過去の記録 ～05/01｜次回の予定｜今後の予定 05/02～
| 開催情報 | 金曜日 13:30～15:00 数理科学研究科棟(駒場) 118号室 |
|---|---|
| 担当者 | 權業 善範、河上 龍郎 、榎園 誠 |
2024年12月20日(金)
13:30-15:00 数理科学研究科棟(駒場) 118号室
榎園誠 氏 (東京大学)
Normal stable degenerations of Noether-Horikawa surfaces
榎園誠 氏 (東京大学)
Normal stable degenerations of Noether-Horikawa surfaces
[ 講演概要 ]
Noether-Horikawa surfaces are surfaces of general type satisfying the equation K2=2pg−4, which represents the boundary of the Noether inequality K2≥2pg−4 for surfaces of general type. In the 1970s, Horikawa conducted a detailed study of smooth Noether-Horikawa surfaces, providing a classification of these surfaces and describing their moduli spaces.
In this talk, I will present an explicit classification of normal stable degenerations of Noether-Horikawa surfaces. Specifically, I will discuss the following results:
(1) A preliminary classification of Noether-Horikawa surfaces with Q-Gorenstein smoothable log canonical singularities.
(2) Several criteria for determining the (global) Q-Gorenstein smoothability of the surfaces described in (1).
(3) Deformation results for Q-Gorenstein smoothable normal stable Noether-Horikawa surfaces, along with a description of the KSBA moduli spaces for these surfaces.
This is joint work with Hiroto Akaike, Masafumi Hattori and Yuki Koto.
Noether-Horikawa surfaces are surfaces of general type satisfying the equation K2=2pg−4, which represents the boundary of the Noether inequality K2≥2pg−4 for surfaces of general type. In the 1970s, Horikawa conducted a detailed study of smooth Noether-Horikawa surfaces, providing a classification of these surfaces and describing their moduli spaces.
In this talk, I will present an explicit classification of normal stable degenerations of Noether-Horikawa surfaces. Specifically, I will discuss the following results:
(1) A preliminary classification of Noether-Horikawa surfaces with Q-Gorenstein smoothable log canonical singularities.
(2) Several criteria for determining the (global) Q-Gorenstein smoothability of the surfaces described in (1).
(3) Deformation results for Q-Gorenstein smoothable normal stable Noether-Horikawa surfaces, along with a description of the KSBA moduli spaces for these surfaces.
This is joint work with Hiroto Akaike, Masafumi Hattori and Yuki Koto.
