Elementary introduction to representable functors and Hilbert schemes

Stein Strømme

Banach Center Publications (1996)

  • Volume: 36, Issue: 1, page 179-198
  • ISSN: 0137-6934

Abstract

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The purpose of this paper is to define and prove the existence of the Hilbert scheme. This was originally done by Grothendieck in [4]. A simplified proof was given by Mumford [11], and we will basically follow that proof, with small modifications.

How to cite

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Strømme, Stein. "Elementary introduction to representable functors and Hilbert schemes." Banach Center Publications 36.1 (1996): 179-198. <http://eudml.org/doc/208577>.

@article{Strømme1996,
abstract = {The purpose of this paper is to define and prove the existence of the Hilbert scheme. This was originally done by Grothendieck in [4]. A simplified proof was given by Mumford [11], and we will basically follow that proof, with small modifications.},
author = {Strømme, Stein},
journal = {Banach Center Publications},
keywords = {existence of Hilbert scheme},
language = {eng},
number = {1},
pages = {179-198},
title = {Elementary introduction to representable functors and Hilbert schemes},
url = {http://eudml.org/doc/208577},
volume = {36},
year = {1996},
}

TY - JOUR
AU - Strømme, Stein
TI - Elementary introduction to representable functors and Hilbert schemes
JO - Banach Center Publications
PY - 1996
VL - 36
IS - 1
SP - 179
EP - 198
AB - The purpose of this paper is to define and prove the existence of the Hilbert scheme. This was originally done by Grothendieck in [4]. A simplified proof was given by Mumford [11], and we will basically follow that proof, with small modifications.
LA - eng
KW - existence of Hilbert scheme
UR - http://eudml.org/doc/208577
ER -

References

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  1. [Baye] D. Bayer, The division algorithm and the Hilbert scheme, Ph.D. thesis, Harvard University, May 1982. 
  2. [Gotz] G. Gotzmann, Eine Bedingung für die Flachheit und das Hilbertpolynom eines graduierten Ringes, Math. Z. 158 (1978), 61-70. Zbl0352.13009
  3. [Gree] M. Green, Restrictions of linear series to hyperplanes, and some results of Macaulay and Gotzmann, in: Algebraic curves and projective geometry, Proceedings, Trento 1988, Lecture Notes in Math. 1389, Springer, Berlin, 1988. 
  4. [Grot-1] A. Grothendieck, Techniques de construction et théorémes d'existence en géométrie algébrique IV: Les schémas de Hilbert, Séminaire Bourbaki 221, 1960/61. 
  5. [Hart-2] R. Hartshorne, Connectedness of the Hilbert scheme, Inst. Hautes Études Sci. Publ. Math. 29 (1966), 261-309. 
  6. [AG] R. Hartshorne, Algebraic Geometry, Graduate Texts in Math. 52, Springer, Berlin, Tokyo, New York, 1977. 
  7. [Klei-2] S. L. Kleiman, Geometry of grassmannians and applications to splitting bundles and smoothing cycles, Inst. Hautes Études Sci. Publ. Math. 36 (1969), 281-297, volume dedicated to Oscar Zariski. Zbl0208.48501
  8. [Laud] O. A. Laudal, Formal Moduli of Algebraic Structures, Lecture Notes in Math. 754 Springer, Berlin-Heidelberg-New York-London-Paris-Tokyo, 1979. 
  9. [Mori] S. Mori, Projective manifolds with ample tangent bundles. Ann. of Math. (2) 110 (1979), 593-606. Zbl0423.14006
  10. [Mumf-3] D. Mumford, Further pathologies in algebraic geometry, Amer. J. Math. 84 (1962), 642-648. Zbl0114.13106
  11. [Mumf-1] D. Mumford, Lectures on Curves on an Algebraic Surface, Studies in Mathematics 59, Princeton University Press, 1968. 
  12. [Red] D. Mumford, The red book of varieties and schemes, Lecture Notes in Math. 1358, Springer, Berlin-Heidelberg-New York-London-Paris-Tokyo, 1988. Zbl0658.14001
  13. [Schl-1] M. Schlessinger, Functors of Artin rings, Trans. Amer. Math. Soc. 130 (1968), 208-222. Zbl0167.49503

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