On the dimension of secant varieties

Chiantini, Luca, and Ciliberto, Ciro. "On the dimension of secant varieties." Journal of the European Mathematical Society 012.5 (2010): 1267-1291. <http://eudml.org/doc/277685>.

@article{Chiantini2010,
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.},
author = {Chiantini, Luca, Ciliberto, Ciro},
journal = {Journal of the European Mathematical Society},
keywords = {higher secant varieties; tangential projections; special varieties; secant varieties; tangential projections; defective varieties},
language = {eng},
number = {5},
pages = {1267-1291},
publisher = {European Mathematical Society Publishing House},
title = {On the dimension of secant varieties},
url = {http://eudml.org/doc/277685},
volume = {012},
year = {2010},
}

TY - JOUR
AU - Chiantini, Luca
AU - Ciliberto, Ciro
TI - On the dimension of secant varieties
JO - Journal of the European Mathematical Society
PY - 2010
PB - European Mathematical Society Publishing House
VL - 012
IS - 5
SP - 1267
EP - 1291
AB - 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.
LA - eng
KW - higher secant varieties; tangential projections; special varieties; secant varieties; tangential projections; defective varieties
UR - http://eudml.org/doc/277685
ER -