Hirzebruch-type inequalities viewed as tools in combinatorics
arXiv:1808.09167 · doi:10.37236/8335
Abstract
The main purpose of this survey is to provide an introduction, algebro-topological in nature, to Hirzebuch-type inequalities for plane curve arrangements in the complex projective plane. These inequalities gain more and more interest due to their utility in many combinatorial problems related to point or line arrangements in the plane. We would like to present a summary of the technicalities and also some recent applications, for instance in the context of the Weak Dirac Conjecture. We also advertise some open problems and questions.
arXiv comment24 pages, the final version incorporating referees' remarks and suggestions, to appear in Electronic Journal of Combinatorics
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