Rocky Mountain Journal of Mathematics

Multigraded Hilbert schemes parametrizing ideals in the Weyl algebra

Jen-Chieh Hsiao

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Abstract

Results of Haiman and Sturmfels \cite {HS04} on multigraded Hilbert schemes are used to establish a quasi-projective scheme which parametrizes all left homogeneous ideals in the Weyl algebra having a fixed Hilbert function with respect to a given grading by an abelian group.

Article information

Source
Rocky Mountain J. Math., Volume 47, Number 8 (2017), 2675-2692.

Dates
First available in Project Euclid: 3 February 2018

Permanent link to this document
https://projecteuclid.org/euclid.rmjm/1517648605

Digital Object Identifier
doi:10.1216/RMJ-2017-47-8-2675

Mathematical Reviews number (MathSciNet)
MR3760312

Zentralblatt MATH identifier
06840994

Subjects
Primary: 14C05: Parametrization (Chow and Hilbert schemes) 16S32: Rings of differential operators [See also 13N10, 32C38]

Keywords
Hilbert schemes Weyl algebras

Citation

Hsiao, Jen-Chieh. Multigraded Hilbert schemes parametrizing ideals in the Weyl algebra. Rocky Mountain J. Math. 47 (2017), no. 8, 2675--2692. doi:10.1216/RMJ-2017-47-8-2675. https://projecteuclid.org/euclid.rmjm/1517648605


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References

  • S.C. Coutinho, A primer of algebraic $D$-modules, Lond. Math. Soc. 33, Cambridge University Press, Cambridge, 1995.
  • Mark Haiman and Bernd Sturmfels, Multigraded Hilbert schemes, J. Alg. Geom. 13 (2004), 725–769.
  • Diane Maclagan, Antichains of monomial ideals are finite, Proc. Amer. Math. Soc. 129 (2001), 1609–1615 (electronic).
  • Mutsumi Saito, Bernd Sturmfels and Nobuki Takayama, Gröbner deformations of hypergeometric differential equations, in Algorithms and computation in mathematics, Volume 6, Springer-Verlag, Berlin, 2000.