Rocky Mountain Journal of Mathematics

Some Amplifications and a Correction of Iarrobino's Construction of Local Parameters on $\text{\rm Hilb}^n_{\P^2_k}$

Mark E. Huibregtse

Full-text: Open access

Article information

Source
Rocky Mountain J. Math., Volume 29, Number 4 (1999), 1321-1361.

Dates
First available in Project Euclid: 5 June 2007

Permanent link to this document
https://projecteuclid.org/euclid.rmjm/1181070410

Digital Object Identifier
doi:10.1216/rmjm/1181070410

Mathematical Reviews number (MathSciNet)
MR1743374

Zentralblatt MATH identifier
0980.14002

Subjects
Primary: 14C05: Parametrization (Chow and Hilbert schemes)

Keywords
Hilbert scheme of points local parameters algebraic surface projective plane

Citation

Huibregtse, Mark E. Some Amplifications and a Correction of Iarrobino's Construction of Local Parameters on $\text{\rm Hilb}^n_{\P^2_k}$. Rocky Mountain J. Math. 29 (1999), no. 4, 1321--1361. doi:10.1216/rmjm/1181070410. https://projecteuclid.org/euclid.rmjm/1181070410


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References

  • A. Altman and S. Kleiman, Introduction to Grothendieck duality theory, Lecture Notes in Math. 146, Springer-Verlag, New York, 1970.
  • J. Briançon, Description de $\textHilb^nC\x,y\$, Invent. Math. 41 (1977), 45-89.
  • J. Cheah, Cellular decompositions for nested Hilbert schemes of points, Pacific J. Math. 183 (1998), 39-90.
  • D. Eisenbud, Commutative algebra with a view toward algebraic geometry, Graduate Texts in Math. 150, Springer-Verlag, New York, 1995.
  • J. Fogarty, Algebraic families on an algebraic surface, Amer. J. Math. 90 (1968), 511-521.
  • A. Grothendieck and J.A. Dieudonne, Eléments de géométrie algébrique I, Springer-Verlag, New York, 1971.
  • M. Haiman, $t,q$-Catalan numbers and the Hilbert scheme, Discrete Math., 193 (1998), 201-224.
  • A. Iarrobino, Punctual Hilbert schemes, Mem. Amer. Math. Soc. 188, Amer. Math. Soc., Providence, RI, 1977.
  • I. Kaplansky, Commutative rings, Allyn and Bacon, Boston, 1970.
  • D. Mumford, Lectures on curves on an algebraic surface, Ann. of Math. Stud., Princeton Univ. Press, Princeton, 1966.
  • M. Schaps, Deformations of Cohen-Macaulay schemes of codimension $2$ and non-singular deformations of space curves, Amer. J. Math. 99 (1977), 669-685.