First we prove that the locus of all sets of fat points with assigned multiplicities whose regularity index is bounded by the so called Segre's bound is open and strictly contains the non-empty open set given by the locus of the same number of fat points with the same multiplicities and support in general position. Then we prove that the the general Segre's bound holds for any set of n+2 fat points of P^n.
Segre's bound and the case of n+2 fat points of P n
BENEDETTI, BEATRICE;FATABBI, Giuliana;LORENZINI, Anna
2012
Abstract
First we prove that the locus of all sets of fat points with assigned multiplicities whose regularity index is bounded by the so called Segre's bound is open and strictly contains the non-empty open set given by the locus of the same number of fat points with the same multiplicities and support in general position. Then we prove that the the general Segre's bound holds for any set of n+2 fat points of P^n.File in questo prodotto:
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