Hilbert Polynomials

  • Joe Harris
Part of the Graduate Texts in Mathematics book series (GTM, volume 133)


Given that a projective variety X ⊂ ℙ n is an intersection of hypersurfaces, one of the most basic problems we can pose in relation to X is to describe the hypersurfaces that contain it. In particular, we want to know how many hypersurfaces of each degree contain X—that is, for each value of m, to know the dimension of the vector space of homogeneous polynomials of degree m vanishing on X.


Complete Intersection Homogeneous Polynomial Projective Variety Betti Number Plane Curve 


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Copyright information

© Springer Science+Business Media New York 1992

Authors and Affiliations

  • Joe Harris
    • 1
  1. 1.Department of MathematicsHarvard UniversityCambridgeUSA

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