JournalsjemsVol. 12 , No. 5DOI 10.4171/jems/229

On the dimension of secant varieties

  • Ciro Ciliberto

    Università di Roma, Italy
  • Luca Chiantini

    Universita di Siena, Italy
On the dimension of secant varieties cover

Abstract

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.