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

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.

The final version incorporating the suggestions of the referees, to appear in Electronic Research Announcements in Mathematical Sciences

References in corpus (3)

• Bounded negativity, Harbourne constants and transversal arrangements of curves
• Invariants of plane curve singularities and Newton diagrams
• A Note on Weak Dirac Conjecture

Cited by in corpus (9)

• Conic-line arrangements in the complex projective plane
• Maximizing curves viewed as free curves
• On plane conic arrangements with nodes and tacnodes
• The 21 reducible polars of Klein's quartic
• $\mathcal{Q}$-conic arrangements in the complex projective plane
• Spanned lines and Langer's inequality
• Hirzebruch-type inequalities viewed as tools in combinatorics
• On the number of ordinary lines determined by sets in complex space
• On combinatorial bounds for the total Tjurina numbers of certain curves and surfaces with isolated singularities