Equality in the Bogomolov–Miyaoka–Yau inequality in the non-general type case-Reference-Cited by-同舟云学术

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

Published:2021-03-12 Issue:0 Volume:0 Page:
ISSN:1435-5345
Container-title:Journal für die reine und angewandte Mathematik
language:en
Short-container-title:

Author:

Hao Feng¹,Schreieder Stefan²

Affiliation:

1. KU Leuven , Celestijnenlaan 200B, B-3001 Leuven , Belgium

2. Institut für Algebraische Geometrie , Leibniz Universität Hannover , Welfengarten 1, 30167 Hannover , Germany

Abstract

Abstract We classify all minimal models X of dimension n, Kodaira dimension n - 1

{n-1}

and with vanishing Chern number c 1 n - 2 ⁢ c 2 ⁢ ( X ) = 0

{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 ϵ > 0

{\epsilon>0}

such that any minimal threefold satisfies either c 1 ⁢ c 2 = 0

{c_{1}c_{2}=0}

or - c 1 ⁢ c 2 > ϵ

{-c_{1}c_{2}>\epsilon}

. This settles completely a conjecture of Kollár.

Publisher

Walter de Gruyter GmbH

Subject

Applied Mathematics,General Mathematics

Reference26 articles.

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