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

Roé, Joaquim

doi:10.1090/S0002-9947-2013-05919-3

Maximal rank for schemes of small multiplicity by Évain’s differential Horace method
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Trans. Amer. Math. Soc. 366 (2014), 857-874 Request permission

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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