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The Chow rings for 3-dimensional toric varieties with one bad isolated singularity

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Abstract

The properties of a toric variety have strong connection with the combinatorial structure of the corresponding fan and the relations among the generators. Using this fact, we have described explicitly the Chow ring for aQ-factorial toric variety as the Stanley-Reisner ring for the corresponding fan modulo the linear equivalence relation. In this paper, we calculate the Chow ring for 3-dimensionalQ-factorial toric varieties having one bad isolated singularity.

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References

  1. L. J. Billera, P. Filliman and B. Sturmfels,Constructions and complexity of secondary polytopes, Adv. in Math.83 (1990), 155–179.

    Article  MATH  MathSciNet  Google Scholar 

  2. V. I. Danilov,The geometry of toric varieties, Uspekhi Mat. Nauk.33 (1978), 85–134.

    MathSciNet  Google Scholar 

  3. W. Fulton,Introduction to Toric Varieties, the 1989 William H. Roever Lecture in Geometry, Washington Univ., St. Louis.

  4. I. M. Gelfand, A. V. Zelevinskij and M. M. Kapranov,Discriminants of polynomials in several variables and triangulations of Newton polyhedra, Leningrad Math. J.2 (1991), 449–505.

    MathSciNet  Google Scholar 

  5. B. Grünbaum,Convex Polytopes, Interscience, London, New York, Sydney, 1969.

    Google Scholar 

  6. P. McMullen,Transforms, diagrams and representations, inContributions to Geometry, Proc. of the Geometry Symp. in Siegen 1978 (J. Tölke and J. M. Wills, eds.), Birkhäuser, Basel, Boston, Stuttgart (1979), 92–130.

    Google Scholar 

  7. T. Oda,Convex Bodies and Algebraic Geometry—An Introduction to the Theory of Toric Varieties, Ergebnisse der Math. (3) 15, Springer-Verlag, Berlin, Heidelberg, New York, London, Paris, Tokyo, 1988.

    Google Scholar 

  8. T. Oda,The intersection cohomology of toric varieties, inThe Geometry of Toric Varieties and Convex Polytopes (T. Hibi ed.), Kokyuroku 776, Research Inst. for Math. Sci., Kyoto Univ., March (1992), 49–67.

  9. T. Oda and H. S. Park,Linear Gale transforms and GKZ decompositions (GKZ is the abbreviation of Gelfand-Kapranov-Zelevinskij), Tohoku Math. J.43 (1991), 375–399.

    Article  MATH  MathSciNet  Google Scholar 

  10. H. S. Park,The Chow rings and GKZ-decompositions for Q-factorial toric varieties, Tohoku Math. J.45 (1993), 109–145.

    Article  MATH  MathSciNet  Google Scholar 

  11. R. P. Stanley,Combinatorics and Commutative Algebra, Progress in math. 41, Birkhäuser, Boston, Basel, Stuttgart, 1983.

    Google Scholar 

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This work was done under the support of the Institute of Basic Science of Seowon University, 1995 grant

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Park, H.S. The Chow rings for 3-dimensional toric varieties with one bad isolated singularity. Korean J. Com. & Appl. Math. 3, 65–78 (1996). https://doi.org/10.1007/BF03028839

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  • DOI: https://doi.org/10.1007/BF03028839

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