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Hilbert Function and Dimension

In: A Singular Introduction to Commutative Algebra

Author

Listed:
  • Gert-Martin Greuel

    (University of Kaiserslautern, Department of Mathematics)

  • Gerhard Pfister

    (University of Kaiserslautern, Department of Mathematics)

Abstract

The Hilbert function of a graded module associates to an integer n the dimension of the n-th graded part of the given module. For sufficiently large n, the values of this function are given by a polynomial, the Hilbert polynomial. To show this, we use the Hilbert-Poincaré series, a formal power series in t with coefficients being the values of the Hilbert function. This power series turns out to be a rational function.

Suggested Citation

  • Gert-Martin Greuel & Gerhard Pfister, 2002. "Hilbert Function and Dimension," Springer Books, in: A Singular Introduction to Commutative Algebra, chapter 5, pages 275-312, Springer.
    • Handle: RePEc:spr:sprchp:978-3-662-04963-1_5
    DOI: 10.1007/978-3-662-04963-1_5
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