# Elementary introduction to representable functors and Hilbert schemes

Banach Center Publications (1996)

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

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topStrømme, 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

top- [Baye] D. Bayer, The division algorithm and the Hilbert scheme, Ph.D. thesis, Harvard University, May 1982.
- [Gotz] G. Gotzmann, Eine Bedingung für die Flachheit und das Hilbertpolynom eines graduierten Ringes, Math. Z. 158 (1978), 61-70. Zbl0352.13009
- [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.
- [Grot-1] A. Grothendieck, Techniques de construction et théorémes d'existence en géométrie algébrique IV: Les schémas de Hilbert, Séminaire Bourbaki 221, 1960/61.
- [Hart-2] R. Hartshorne, Connectedness of the Hilbert scheme, Inst. Hautes Études Sci. Publ. Math. 29 (1966), 261-309.
- [AG] R. Hartshorne, Algebraic Geometry, Graduate Texts in Math. 52, Springer, Berlin, Tokyo, New York, 1977.
- [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
- [Laud] O. A. Laudal, Formal Moduli of Algebraic Structures, Lecture Notes in Math. 754 Springer, Berlin-Heidelberg-New York-London-Paris-Tokyo, 1979.
- [Mori] S. Mori, Projective manifolds with ample tangent bundles. Ann. of Math. (2) 110 (1979), 593-606. Zbl0423.14006
- [Mumf-3] D. Mumford, Further pathologies in algebraic geometry, Amer. J. Math. 84 (1962), 642-648. Zbl0114.13106
- [Mumf-1] D. Mumford, Lectures on Curves on an Algebraic Surface, Studies in Mathematics 59, Princeton University Press, 1968.
- [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
- [Schl-1] M. Schlessinger, Functors of Artin rings, Trans. Amer. Math. Soc. 130 (1968), 208-222. Zbl0167.49503

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