On Hirzebruch Type Inequalities and Applications

Szpond, Justyna

doi:10.1007/978-3-030-00027-1_14

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Arrangements In the Real Projective Plane1

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2019

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“…Melchior's result shows that a non-trivial real line arrangement must not only have positive t 2 but in fact there must be at least 3 double points. Interesting generalizations of Melchior's inequality in the realms of complex line arrangements have been obtained by Hirzebruch [27], see also [39] and the article by Piotr Pokora in this volume [36].…”

Section: Arrangements In the Real Projective Planementioning

confidence: 92%

A few introductory remarks on line arrangements

Szpond¹

2019

Analytic and Algebraic Geometry 3

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Points and lines can be regarded as the simplest geometrical objects. Incidence relations between them have been studied since ancient times. Strangely enough our knowledge of this area of mathematics is still far from being complete. In fact a number of interesting and apparently difficult conjectures has been raised just recently. Additionally a number of interesting connections to other branches of mathematics have been established. This is an attempt to record some of these recent developments. 2010 Mathematics Subject Classification. 14C20 and MSC 14N20 and MSC 13A15.

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Section: Arrangements In the Real Projective Planementioning

confidence: 92%