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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Maximal rank for schemes of small multiplicity by Évain's differential Horace method


Author: Joaquim Roé
Journal: Trans. Amer. Math. Soc. 366 (2014), 857-874
MSC (2010): Primary 14C20; Secondary 14H20, 14H50, 14D06
Published electronically: September 26, 2013
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Abstract: The Hilbert function of the union of $ n$ general $ e$-fold points in the plane is maximal if $ n\ge 4e^2$ or $ n$ is a square. The Hilbert function of a union of $ A$, $ D$, $ E$ singularity schemes in general position is maximal in every degree $ >28$. The proofs use a computation of limits of families of linear systems whose special members acquire base divisors, an interesting problem in itself.


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Additional Information

Joaquim Roé
Affiliation: Department of Mathematics, Universitat Autònoma de Barcelona, 08193 Barcelona, Spain

DOI: http://dx.doi.org/10.1090/S0002-9947-2013-05919-3
PII: S 0002-9947(2013)05919-3
Received by editor(s): October 16, 2009
Received by editor(s) in revised form: May 14, 2012
Published electronically: September 26, 2013
Additional Notes: The author was partially supported by the Spanish Ministerio de ciecia e innovación grant MTM 2009-10359
Article copyright: © Copyright 2013 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.