Implicitization using approximation complexes

  • Marc Chardin
Part of the Mathematics and Visualization book series (MATHVISUAL)


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  1. 1.
    R. Goldman, R. Krasaukas (Eds.). Topics in Algebraic Goemetry and Geometric Modeling. Contemporary Mathematics 334 (2003).Google Scholar
  2. 2.
    L. Busé. Algorithms for the implicitization using approximation complexes. (
  3. 3.
    L. Busé, M. Chardin. Implicitizing rational hypersurfaces using approximation complexes. J. Symbolic Computation (to appear).Google Scholar
  4. 4.
    L. Busé, D. Cox, C. D’Andréa. Implicitization of surfaces in P3 in the presence of base points. J. Algebra Appl. 2 (2003), 189-214.zbMATHCrossRefMathSciNetGoogle Scholar
  5. 5.
    L. Busé, J.-P. Jouanolou. On the closed image of a rational map and the implicitization problem. J. Algebra 265 (2003), 312-357.zbMATHCrossRefMathSciNetGoogle Scholar
  6. 6.
    M. Chardin. Regularity of ideals and their powers. Preprint 364 (Mars 2004), Institut de Mathématiques de Jussieu, Paris.Google Scholar
  7. 7.
    D. Cox. Equations of parametric curves and surfaces via syzygies. Contemporary Mathematics 286 (2001), 1-20.Google Scholar
  8. 8.
    D. Cox, T. Sederberg, F. Chen. The moving line ideal basis of planar rational curves. Comp. Aid. Geom. Des. 15 (1998), 803-827.zbMATHCrossRefMathSciNetGoogle Scholar
  9. 9.
    D. Cox, R. Goldman, M. Zhang On the validity of implicitization by moving quadrics for rationnal surfaces with no base points. J. Symbolic Computation 29(2000),419-440.zbMATHCrossRefMathSciNetGoogle Scholar
  10. 10.
    C. D’Andréa. Resultants and moving surfaces. J. of Symbolic Computation 31 (2001),585-602.zbMATHCrossRefGoogle Scholar
  11. 11.
    D. Eisenbud. Commutative algebra. With a view toward algebraic geometry. Graduate Texts in Mathematics 150. Springer-Verlag, New York, 1995.Google Scholar
  12. 12.
    W. Fulton. Intersection theory. Second edition. Ergebnisse der Mathematik und ihrer Grenzgebiete 3. Springer-Verlag, Berlin, 1998.Google Scholar
  13. 13.
    I. M. Gel’fand, M. Kapranov, A. Zelevinsky. Discriminants, resultants, and mul-tidimensional determinants. Mathematics: Theory & Applications. Birkhäuser Boston, Inc., Boston, MA, 1994.CrossRefGoogle Scholar
  14. 14.
    D. Grayson, M. Stillman. Macaulay 2. (
  15. 15.
    R. Hartshorne. Algebraic geometry. Graduate Texts in Mathematics52. Springer-Verlag, New York-Heidelberg, 1977.Google Scholar
  16. 16.
    D. G. Northcott. Finite free resolutions. Cambridge Tracts in Mathematics 71. Cambridge University Press, Cambridge-New York-Melbourne, 1976.Google Scholar
  17. 17.
    T. Sederberg, F. Chen. Implicitization using moving curves and surfaces. Pro-ceedings of SIGGRAPH 95, Addison Wesley, 1995, 301-308.Google Scholar
  18. 18.
    W. Vasconcelos. The Arithmetic of Blowup Algebras. London Math. Soc. Lecture Note Ser. 195. Cambridge University Press, 1994.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Marc Chardin
    • 1
  1. 1.Institut de Mathématiques de JussieuParisFrance

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