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Mathematische Zeitschrift

, Volume 275, Issue 1–2, pp 529–548 | Cite as

Segre classes on smooth projective toric varieties

  • Torgunn Karoline MoeEmail author
  • Nikolay Qviller
Article

Abstract

We provide a generalization of the algorithm of Eklund, Jost and Peterson for computing Segre classes of closed subschemes of projective \(k\)-space. The algorithm is here generalized to computing the Segre classes of closed subschemes of smooth projective toric varieties.

Keywords

Segre classes Toric varieties Computational algorithm Nef cone Intersection theory 

Mathematics Subject Classification (2000)

Primary 14C17 14M25 Secondary 14C20 14Q99 

Notes

Acknowledgments

We want to thank Ragni Piene for valuable supervision, Christine Jost for comments and for pointing us towards the Sage [12] implementation of intersection theory in the toric setting, and Kristian Ranestad for reminding us of the importance of nefness. Furthermore, we are grateful to Carel Faber and the referee for constructive remarks and comments. Finally, we want to thank Terje Kvernes at Drift and Georg Muntingh for computer assistance. All computations are performed using Macaulay2 [8] by Grayson and Stillman with the module NormalToricVarieties by Smith, and Sage [12] by Stein et al.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of OsloOsloNorway

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