Equality in the Bogomolov–Miyaoka–Yau inequality in the non-general type case

Publikation: Beitrag in Fachzeitschrift › Artikel › Forschung › Peer-Review

Autoren

  • Feng Hao
  • Stefan Schreieder

Organisationseinheiten

Externe Organisationen

  • KU Leuven
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Details

OriginalspracheEnglisch
Seiten (von - bis)87-115
Seitenumfang29
FachzeitschriftJ REINE ANGEW MATH
Jahrgang2021
Ausgabenummer775
Frühes Online-Datum12 März 2021
PublikationsstatusVeröffentlicht - 1 Juni 2021

Abstract

We classify all minimal models X of dimension n, Kodaira dimension n-1 and with vanishing Chern number \(c_1^{n-2}c_2(X)=0\). This solves a problem of Kollár. Completing previous work of Kollár and Grassi, we also show that there is a universal constant \(\epsilon>0\) such that any minimal threefold satisfies either \(c_1c_2=0\) or \(-c_1c_2>\epsilon\). This settles completely a conjecture of Kollár.

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Equality in the Bogomolov–Miyaoka–Yau inequality in the non-general type case. / Hao, Feng; Schreieder, Stefan.
in: J REINE ANGEW MATH, Jahrgang 2021, Nr. 775, 01.06.2021, S. 87-115.

Publikation: Beitrag in Fachzeitschrift › Artikel › Forschung › Peer-Review

Hao F, Schreieder S. Equality in the Bogomolov–Miyaoka–Yau inequality in the non-general type case. J REINE ANGEW MATH. 2021 Jun 1;2021(775):87-115. Epub 2021 Mär 12. doi: 10.1515/crelle-2021-0008
Hao, Feng ; Schreieder, Stefan. / Equality in the Bogomolov–Miyaoka–Yau inequality in the non-general type case. in: J REINE ANGEW MATH. 2021 ; Jahrgang 2021, Nr. 775. S. 87-115.
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abstract = "We classify all minimal models X of dimension n, Kodaira dimension n-1 and with vanishing Chern number \(c_1^{n-2}c_2(X)=0\). This solves a problem of Koll{\'a}r. Completing previous work of Koll{\'a}r and Grassi, we also show that there is a universal constant \(\epsilon>0\) such that any minimal threefold satisfies either \(c_1c_2=0\) or \(-c_1c_2>\epsilon\). This settles completely a conjecture of Koll{\'a}r.",
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