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

Piotr Pokora

doi:10.3934/era.2017.24.003

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2017, Volume 24: 21-27. Doi: 10.3934/era.2017.24.003

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

Piotr Pokora

1.
Instytut Matematyki, Pedagogical University of Cracow, Podchorążych 2, PL-30-084 Kraków, Poland
2.
Institut für Algebraische Geometrie, Leibniz Universität Hannover, Welfengarten 1, D-30167 Hannover, Germany

To Professor Kamil Rusek, on the occasion of his 70th birthday.

Received: December 26, 2016

Published: August 2017

I am very grateful to Adrian Langer for stimulating conversations, useful comments about the content of the note, and for pointing out [2]. Finally, I would like to thank the anonymous referees for valuable comments that allowed to improve the note. The author is partially supported by National Science Centre Poland Grant 2014/15/N/ST1/02102.

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Abstract

Using Langer's variation on the Bogomolov-Miyaoka-Yau inequality, we provide some Hirzebruch-type inequalities for curve arrangements in the complex projective plane.

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Mathematics Subject Classification: 52C35, 14C20, 32S22.

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References

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