Chern class inequalities for non-uniruled projective varieties

TL;DR

This paper extends the Miyaoka-Yau inequalities, originally valid for projective minimal models, to all smooth, projective, non-uniruled varieties, broadening their applicability in algebraic geometry.

Contribution

The authors generalize the Miyaoka-Yau inequalities to a wider class of varieties beyond minimal models, specifically to all smooth, projective, non-uniruled varieties.

Findings

Miyaoka-Yau inequalities hold for non-uniruled varieties

Extension of inequalities to broader class of varieties

Potential implications for classification of algebraic varieties

Abstract

It is known that projective minimal models satisfy the celebrated Miyaoka-Yau inequalities. In this article, we extend these inequalities to the set of all smooth, projective and non-uniruled varieties.