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Geography of Gorenstein stable log surfaces


Authors: Wenfei Liu and Sönke Rollenske
Journal: Trans. Amer. Math. Soc. 368 (2016), 2563-2588
MSC (2010): Primary 14J10, 14J29
DOI: https://doi.org/10.1090/tran/6404
Published electronically: July 10, 2015
MathSciNet review: 3449249
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Abstract | References | Similar Articles | Additional Information

Abstract: We study the geography of Gorenstein stable log surfaces and prove two inequalities for their invariants: the stable Noether inequality and the $ P_2$-inequality.

By constructing examples we show that all invariants are realised except possibly some cases where the inequalities become equalities.


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Additional Information

Wenfei Liu
Affiliation: Institut für algebraische Geometrie, Gottfried Wilhelm Leibniz Universität Hannover, Welfengarten 1, 30167 Hannover, Germany
Address at time of publication: School of Mathematical Sciences and BICMR, Peking University, Yiheyuan Road 5, Haidian District, Beijing 100871, People’s Republic of China
Email: wliu@math.uni-hannover.de, wliu@math.pku.edu.cn

Sönke Rollenske
Affiliation: Fakultät für Mathematik, Universtät Bielefeld, Universitätsstrasse 25, 33615 Bielefeld, Germany
Address at time of publication: FB 12 / Mathematik und Informatik, Philipps-Universität Marburg, Hans-Meerwein-Strasse 6/ Campus Lahnberge, 35032 Marburg, Germany
Email: rollenske@math.uni-bielefeld.de, rollenske@mathematik.uni-marburg.de

DOI: https://doi.org/10.1090/tran/6404
Keywords: Stable surface, stable log surface, geography of surfaces
Received by editor(s): August 20, 2013
Received by editor(s) in revised form: January 23, 2014
Published electronically: July 10, 2015
Additional Notes: The first author was supported by the Bielefelder Nachwuchsfonds
Both authors were supported by DFG via the second author’s Emmy-Noether project and partially via SFB 701
Article copyright: © Copyright 2015 American Mathematical Society

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