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Zariski chambers on surfaces of high Picard number

Part of: Cycles and subschemes Computational aspects in algebraic geometry

Published online by Cambridge University Press:  01 August 2012

Thomas Bauer  and
David Schmitz
Thomas Bauer
Affiliation:
Fachbereich Mathematik und Informatik, Philipps-Universität Marburg, Hans-Meerwein-Straße D-35032 Marburg, Germany (email: tbauer@mathematik.uni-marburg.de)
David Schmitz
Affiliation:
Fachbereich Mathematik und Informatik, Philipps-Universität Marburg, Hans-Meerwein-Straße D-35032 Marburg, Germany (email: schmitzd@mathematik.uni-marburg.de)

Abstract

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We present an improved algorithm for the computation of Zariski chambers on algebraic surfaces. The new algorithm significantly outperforms the currently available method and therefore allows us to treat surfaces of high Picard number, where huge numbers of chambers occur. As an application, we efficiently compute the number of chambers supported by the lines on the Segre–Schur quartic.

MSC classification

Secondary: 14C20: Divisors, linear systems, invertible sheaves 14Q10: Surfaces, hypersurfaces
Type
Research Article
Information
LMS Journal of Computation and Mathematics , Volume 15 , May 2012 , pp. 219 - 230
Copyright
Copyright © London Mathematical Society 2012

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