Author:
Ballico Edoardo,Chiantini Luca
Abstract
AbstractWe introduce and study properties of the Terracini locus of projective
varieties X, which is the locus of finite sets $$S \subset X$$
S
⊂
X
such that 2S fails to impose
independent conditions to a linear system L. Terracini loci are relevant in the
study of interpolation problems over double points in special position, but they
also enter naturally in the study of special loci contained in secant varieties to
projective varieties.We find some criteria which exclude that a set S belongs to the Terracini
locus. Furthermore, in the case where X is a Veronese variety, we bound the
dimension of the Terracini locus and we determine examples in which the locus
has codimension 1 in the symmetric product of X.
Funder
Università degli Studi di Siena
Publisher
Springer Science and Business Media LLC
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