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Algebraic Surfaces in Positive Characteristic

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Birational Geometry, Rational Curves, and Arithmetic

Abstract

These notes grew out of a series of lectures given at Sogang University, Seoul, in October 2009. They were meant for complex geometers, who are not familiar with characteristic-p-geometry but who would like to see similarities, as well as differences, to complex geometry. More precisely, these notes are on algebraic surfaces in positive characteristic and assume familiarity with the complex side of this theory, say, on the level of Beauville’s book [9].

Mathematics Subject Classification codes (2010): 14-02, 14J10, 14G17.

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Acknowledgements

These lecture notes grew out of a lecture series given at Sogang University, Seoul, in October 19–22, 2009. I thank Yongnam Lee for the invitation to Sogang University and hospitality. It was a pleasure visiting him and giving these lectures. Also, I thank Fabrizio Catanese, Hisanori Ohashi, Holger Partsch, Sönke Rollenske, Nguyen Le Dang Thi, Yuri Tschinkel, Tong Zhang, and the referee for suggestions, remarks, and pointing out mistakes in earlier versions. I thank the referee especially for clarifications and providing me with more references. I wrote up a first version of these notes at Stanford University and I thank the department for hospitality. I gratefully acknowledge funding from DFG under research grants LI 1906/1-1 and LI 1906/1-2.

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  1. Mathematisches Institut, Endenicher Allee 60, D-53115, Bonn, Germany

    Christian Liedtke

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  1. Christian Liedtke
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Correspondence to Christian Liedtke .

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  1. Department of Mathematics, Courant Institute of Math. Sciences, New York University, Mercer St. 251, New York, 10012, New York, USA

    Fedor Bogomolov

  2. , Department of Mathematics, Rice University, S. Main St. 6100, Houston, 77251-1892, Texas, USA

    Brendan Hassett

  3. Department of Mathematics, Courant Institute of Math. Sciences, New York University, Mercer St. 251, New York, 10012, New York, USA

    Yuri Tschinkel

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Liedtke, C. (2013). Algebraic Surfaces in Positive Characteristic. In: Bogomolov, F., Hassett, B., Tschinkel, Y. (eds) Birational Geometry, Rational Curves, and Arithmetic. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-6482-2_11

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