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 ≥ 4e2 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. ©2013 American Mathematical Society.
Original languageEnglish
Pages (from-to)857-874
JournalTransactions of the American Mathematical Society
Volume366
DOIs
Publication statusPublished - 1 Jan 2014

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