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A brief proof of a maximal rank theorem for generic double points in projective space
Author(s):
Karen
A.
Chandler
Journal:
Trans. Amer. Math. Soc.
353
(2001),
1907-1920.
MSC (1991):
Primary 13D40, 14F17
Posted:
December 21, 2000
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Abstract:
We give a simple proof of the following theorem of J. Alexander and A. Hirschowitz: Given a general set of points in projective space, the homogeneous ideal of polynomials that are singular at these points has the expected dimension in each degree of 4 and higher, except in 3 cases.
References:
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- [A]
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- J. Alexander, A. Hirschowitz, La méthode d'Horace éclatée: application à l'interpolation en degré quatre, Invent. Math. 107, 585-602 (1992). MR 93d:13017
- [AH3]
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- [AH4]
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- [AH5]
- J. Alexander, A. Hirschowitz, An asymptotic vanishing theorem for generic unions of multiple points, Invent. Math. 140 (2000), 303-325. CMP 2000:12
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- M.V. Catalisano, N.V. Trung, G. Valla, A sharp bound for the regularity index of fat points in general position, Proc. Amer. Math. Soc. 118 (1993), 717-724. MR 93i:13021
- [C1]
- K. Chandler, Hilbert functions of dots in linear general position, Zero-Dimensional Schemes (Ravello, 1992), de Gruyter, Berlin, 1994, pp. 65-79. MR 95h:13014
- [C2]
- K. Chandler, Higher infinitesimal neighbourhoods, J. Algebra 205 (1998), 460-479. MR 99c:13036
- [C3]
- K. Chandler, The exceptional cases for general double points, preprint.
- [H]
- A. Hirschowitz, La méthode d'Horace pour l'interpolation à plusieurs variables, Manuscripta Math. 50 (1985), 337-388. MR 86j:14013
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Additional Information:
Karen
A.
Chandler
Affiliation:
Department of Mathematics, University of Notre Dame, Notre Dame, Indiana 46556
Email:
kchandle@noether.math.nd.edu
DOI:
10.1090/S0002-9947-00-02732-X
PII:
S 0002-9947(00)02732-X
Received by editor(s):
October 30, 1999
Received by editor(s) in revised form:
December 7, 1999
Posted:
December 21, 2000
Dedicated:
To A. V. Geramita
Copyright of article:
Copyright
2000,
American Mathematical Society
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