# An improved bound for the degree of smooth surfaces in ${\mathbf{P}}^{4}$ not of general type

Compositio Mathematica (1996)

- Volume: 102, Issue: 2, page 141-145
- ISSN: 0010-437X

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topCook, Michele. "An improved bound for the degree of smooth surfaces in $\mathbf {P}^4$ not of general type." Compositio Mathematica 102.2 (1996): 141-145. <http://eudml.org/doc/90450>.

@article{Cook1996,

author = {Cook, Michele},

journal = {Compositio Mathematica},

keywords = {number of components of the Hilbert scheme; bound for the degree of surfaces not of general type},

language = {eng},

number = {2},

pages = {141-145},

publisher = {Kluwer Academic Publishers},

title = {An improved bound for the degree of smooth surfaces in $\mathbf \{P\}^4$ not of general type},

url = {http://eudml.org/doc/90450},

volume = {102},

year = {1996},

}

TY - JOUR

AU - Cook, Michele

TI - An improved bound for the degree of smooth surfaces in $\mathbf {P}^4$ not of general type

JO - Compositio Mathematica

PY - 1996

PB - Kluwer Academic Publishers

VL - 102

IS - 2

SP - 141

EP - 145

LA - eng

KW - number of components of the Hilbert scheme; bound for the degree of surfaces not of general type

UR - http://eudml.org/doc/90450

ER -

## References

top- [BS] Bayer, D. and Stillman, M.: "A criterion for detecting m-regularity", Invent. Math.87 (1987) 1-11. Zbl0625.13003MR862710
- [BF] Braun, R. and Fløystad, G.: "A bound for the degree of smooth surfaces in P4 not of general type", Compositio Mathematica, Vol. 93, No. 2, September(I) 1994,211-229. Zbl0823.14021MR1287697
- [EP] Ellingsrud, G. and Peskine, C.: "Sur les surfaces lisses de P4", Invent. Math.95 (1989) 1-11. Zbl0676.14009MR969410
- [GLP] Gruson, L., Lazarsfeld, R. and Peskine, C.: "On a Theorem of Castelnuovo, and the equations defining space curves", Invent. Math.72 (1983) 491-506. Zbl0565.14014MR704401
- [GP] Gruson, L. and Peskine, C.: "Genres des courbes de 1'espace projectif ", Lecture Notes in Mathematics, Algebraic Geometry, TromsØ1977, 687 (1977) 31-59. Zbl0412.14011MR527229
- [H] Hartshorne, R.: Algebraic Geometry, Springer-Verlag (1977). Zbl0367.14001MR463157

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