Geodesic
On the dimension of secant varieties
Journal of the European Mathematical Society, Tome 12 (2010) no. 5, pp. 1267-1291

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In this 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 assumptions on X, and we classify varieties for which the bound is attained.
DOI : 10.4171/jems/229
Classification : 14-XX, 00-XX
Keywords: Higher secant varieties, tangential projections, special varieties 
Luca Chiantini; Ciro Ciliberto. On the dimension of secant varieties. Journal of the European Mathematical Society, Tome 12 (2010) no. 5, pp. 1267-1291. doi: 10.4171/jems/229
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