The orbifold Langer-Miyaoka-Yau inequality and Hirzebruch-type inequalities

TL;DR

This paper extends the classical inequalities in algebraic geometry by applying Langer's variation of the Bogomolov-Miyaoka-Yau inequality to derive new Hirzebruch-type inequalities for curve arrangements in the complex projective plane.

Contribution

It introduces novel Hirzebruch-type inequalities using Langer's variation of the Bogomolov-Miyaoka-Yau inequality, expanding the understanding of curve arrangements.

Findings

Derived new inequalities for curve arrangements in the complex projective plane.

Extended classical algebraic geometry inequalities using Langer's approach.

Provided theoretical bounds relevant to complex algebraic surfaces.

Abstract

Using Langer's variation on the Bogomolov-Miyaoka-Yau inequality \cite[Theorem 0.1]{Langer} we provide some Hirzebruch-type inequalities for curve arrangements in the complex projective plane.