Maximal rank for schemes of small multiplicity by Évain’s differential Horace method
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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.References
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Additional Information
- Joaquim Roé
- Affiliation: Department of Mathematics, Universitat Autònoma de Barcelona, 08193 Barcelona, Spain
- ORCID: 0000-0003-0033-8442
- 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
- © Copyright 2013
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Trans. Amer. Math. Soc. 366 (2014), 857-874
- MSC (2010): Primary 14C20; Secondary 14H20, 14H50, 14D06
- DOI: https://doi.org/10.1090/S0002-9947-2013-05919-3
- MathSciNet review: 3130319