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Foundations of Computational Mathematics

, Volume 19, Issue 2, pp 245–258 | Cite as

Complexity Classes and Completeness in Algebraic Geometry

  • M. Umut IsikEmail author
Article
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Abstract

We study the computational complexity of sequences of projective varieties. We define analogues of the complexity classes P and NP for these and prove the NP-completeness of a sequence called the universal circuit resultant. This is the first family of compact spaces shown to be NP-complete in a geometric setting.

Keywords

Complexity classes Completeness Resultant 

Mathematics Subject Classification

14Q20 68Q15 

Notes

Acknowledgements

I would like to thank Vladimir Baranovsky and Saugata Basu for useful discussions on the subject of this paper.

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Copyright information

© SFoCM 2018

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of California, IrvineIrvineUSA

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