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Forum Mathematicum

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Volume 28, Issue 6 (Nov 2016)


When are Zariski chambers numerically determined?

Sławomir Rams
  • Institute of Mathematics, Jagiellonian University, ul. Łojasiewicza 6, 30-348 Kraków, Poland; and Institut für Algebraische Geometrie, Leibniz Universität, Welfengarten 1, 30167 Hannover, Germany
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/ Tomasz SzembergORCID iD: http://orcid.org/0000-0002-4234-5838
Published Online: 2016-05-01 | DOI: https://doi.org/10.1515/forum-2015-0087


The big cone of every smooth projective surface X admits a natural decomposition into Zariski chambers. The purpose of this note is to give a simple criterion for the interiors of all Zariski chambers on X to be numerically determined Weyl chambers. Such a criterion generalizes the results of Bauer–Funke [4] on K3 surfaces to arbitrary smooth projective surfaces. In the last section, we study the relation between decompositions of the big cone and elliptic fibrations on some surfaces.

Keywords: Zariski decomposition; big cone; elliptic fibration

MSC 2010: 14C20; 14J28


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About the article

Received: 2015-05-12

Revised: 2015-11-28

Published Online: 2016-05-01

Published in Print: 2016-11-01

Funding Source: Narodowe Centrum Nauki

Award identifier / Grant number: N N201 608040

Award identifier / Grant number: 2014/15/B/ST1/02197

The work was partially supported by National Science Centre, Poland, grant no. N N201 608040 (first author) and grant no. 2014/15/B/ST1/02197 (second author).

Citation Information: Forum Mathematicum, ISSN (Online) 1435-5337, ISSN (Print) 0933-7741, DOI: https://doi.org/10.1515/forum-2015-0087.

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