|
On the plane section of an integral curve in positive characteristic
Author(s):
Paola
Bonacini
Journal:
Proc. Amer. Math. Soc.
136
(2008),
2289-2297.
MSC (2000):
Primary 14H50;
Secondary 13D40
Posted:
March 19, 2008
Retrieve article in:
PDF
Abstract |
References |
Similar articles |
Additional information
Abstract:
If  is an integral curve and  an algebraically closed field of characteristic 0, it is known that the points of the general plane section  of  are in uniform position. From this it follows easily that the general minimal curve containing  is irreducible. If char , the points of  may not be in uniform position. However, we prove that the general minimal curve containing  is still irreducible.
References:
-
- 1.
- P. Bonacini, Hilbert functions of decreasing type in positive characteristic, to appear in Rend. Sem. Mat. Univ. Pol. Torino.
- 2.
- A. V. Geramita, P. Maroscia, The ideal of forms vanishing at a finite set of points in
 , J. Alg. 90 (1984), 528-555. MR 760027 (86e:14025) - 3.
- A. V. Geramita, P. Maroscia, L. G. Roberts, The Hilbert function of a reduced k-algebra, J. London Math. Soc. (2) 28 (1983), 443-452. MR 724713 (85c:13018)
- 4.
- A. Grothendieck, Éléments de géométrie algébrique: IV. Étude locale de schémas et des morphismes de schémas, Seconde Partie, Publ. Math. IHES 24, 1965.
- 5.
- L. Gruson, C. Peskine, Genre de courbes de l'espace projectif, Algebraic geometry (Proc. Sympos., Univ. Tromsø, Tromsø, 1977), pp. 31-59, Lecture Notes in Math. 687, Springer, Berlin, 1978. MR 0527229 (81e:14019)
- 6.
- L. Gruson, C. Peskine, Section plane d'une courbe gauche: postulation, Progress in Math. 24, Birkhäuser, Boston, MA (1982), 33-35. MR 0685762 (84c:14045)
- 7.
- J. Harris, The genus of space curves, Math. Ann. 249 (1980), 191-204. MR 579101 (81i:14022)
- 8.
- R. Hartshorne, Algebraic Geometry, Graduate Texts in Mathematics 52, Springer-Verlag, New York-Heidelberg, 1977. MR 0463157 (57:3116)
- 9.
- J.-P. Jouanolou, Théorèmes de Bertini et Applications, Progress in Mathematics 42, Birkhäuser Boston, Boston, MA, 1983. MR 725671 (86b:13007)
- 10.
- R. Maggioni, A. Ragusa, Connections between Hilbert function and geometric properties for a finite set of points in
 , Matematiche (Catania) 39 (1984), 153-170. MR 934156 (89c:14046) - 11.
- R. Maggioni, A. Ragusa, Nonsingular curves passing through points of
 in generic position, I, J. Alg. 92 (1985), 176-193. MR 772479 (86c:14026) - 12.
- R. Maggioni, A. Ragusa, The Hilbert function of generic plane sections of curves in
 , Inv. Math. 91 (1988), 253-258. MR 922800 (89g:14027) - 13.
- J. S. Milne, Étale cohomology, Princeton Mathematical Series 33, Princeton University Press, Princeton, NJ, 1980. MR 559531 (81j:14002)
- 14.
- J. Rathmann, The uniform position lemma for curves in characteristic p, Math. Ann. 276 (1987), 565-579. MR 879536 (89g:14026)
- 15.
- I. R. Shafarevich, Basic Algebraic Geometry I--Varieties in Projective Space, 2nd rev. and exp. ed., Springer-Verlag, Berlin-Heidelberg, 1994. MR 1328833 (95m:14001)
Similar Articles:
Retrieve articles in Proceedings of the American Mathematical Society
with MSC
(2000):
14H50,
13D40
Retrieve articles in all Journals with MSC
(2000):
14H50,
13D40
Additional Information:
Paola
Bonacini
Affiliation:
Dipartimento di Matematica e Informatica, Università degli Studi di Catania, Viale A. Doria 6, 95125 Catania, Italy
Email:
bonacini@dmi.unict.it
DOI:
10.1090/S0002-9939-08-09271-X
PII:
S 0002-9939(08)09271-X
Keywords:
Integral curve,
plane section,
minimal curve,
positive characteristic
Received by editor(s):
July 26, 2006,
Received by editor(s) in revised form:
February 19, 2007
Posted:
March 19, 2008
Communicated by:
Ted Chinburg
Copyright of article:
Copyright
2008,
American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.
|
Comments: webmaster@ams.org