On the Dimension of Secant Varieties

Mathematics – Algebraic Geometry

Scientific paper

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Scientific paper

We generalize Zak's theorems on tangencies and on linear normality as well as
Zak's definition and classification of Severi varieties. In particular we find
sharp lower bounds for the dimension of higher secant varieties of a given
variety X under suitable regularity assumption on X, and we classify varieties
for which the bound is attained.

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