ScholarLens Back to search
2020•arXiv (Cornell University)Open access

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

Feng Hao, Stefan Schreieder

Open full text 0 citations

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 $ε>0$ such that any minimal threefold satisfies either $c_1c_2=0$ or $-c_1c_2>ε$. This settles completely a conjecture of Kollár.

Open-access reader

About this research paper

What this paper is about

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 $ε>0$ such that any minimal threefold satisfies either $c_1c_2=0$ or $-c_1c_2>ε$. This settles completely a conjecture of Kollár.

Why it matters

A significance statement is not available in the OpenAlex record.

Key contribution

A contribution statement is not available in the OpenAlex record.

Method / approach

Method details are not available in the OpenAlex metadata.

Main findings

Findings are not separately available in the OpenAlex metadata.

Limitations

Limitations are not available in the OpenAlex metadata.

Applications

Application details are not available in the OpenAlex metadata.

Available 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 $ε>0$ such that any minimal threefold satisfies either $c_1c_2=0$ or $-c_1c_2>ε$. This settles completely a conjecture of Kollár.

Key concepts: Kodaira dimension, Dimension (graph theory), Conjecture, Mathematics, Type (biology), Constant (computer programming), Pure mathematics, Inequality

Related papers

Related paper 1Related paper 2Related paper 3
Back to paper searchBrowse research topicsOriginal source
Equality in the Bogomolov--Miyaoka--Yau inequality in the non-general type case — Research Paper | ScholarLens