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A Solution to Hironaka’s Polyhedra Game

  • Mark Spivakovsky
Part of the Progress in Mathematics book series (PM, volume 36)

Abstract

In this paper we present a solution to Hironaka’s polyhedra game. That is, we prove the existence of a winning strategy for the first player.

Keywords

Convex Hull Algebraic Variety Infinite Sequence Finite Sequence Winning Strategy 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. [1]
    Hironaka, H., “Characteristic polyhedra of singularities,” Journal of Mathematics of Kyoto University, Vol. 7, 1968, pp. 251–293.MathSciNetGoogle Scholar
  2. [2]
    Hironaka, H., “Study of Algebraic Varieties” (in Japanese), Monthly Report, Japan Acad., Vol. 23, No. 5, 1970, pp. 1–5.Google Scholar
  3. [3]
    Hironaka, H., “Schemes, ETC,” Proc. 5th Nordic Summer School in Math., Oslo, 1970, pp. 291–313.Google Scholar
  4. [4]
    Hironaka, H., “Certain numerical characters of singularities,” Journal of Mathematics of Kyoto University, Vol. 10, 1970, pp. 151–187.MathSciNetzbMATHGoogle Scholar
  5. [5]
    Spivakovsky, M., “A counterexample to Hironaka’s ”hard“ polyhedra game,” to appear in the Journal of Mathematics of Kyoto University.Google Scholar

Copyright information

© Springer Science+Business Media New York 1983

Authors and Affiliations

  • Mark Spivakovsky
    • 1
    • 2
  1. 1.Department of MathematicsHarvard UniversityCambridgeUSA
  2. 2.Research Institute of Mathematical ScienceKyotoJapan

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