# IJPAM: Volume 50, No. 3 (2009)

ON THE SECANT VARIETIES TO THE TANGENT
DEVELOPABLE OF VERONESE VARIETIES

E. Ballico
Department of Mathematics
University of Trento
380 50 Povo (Trento) - Via Sommarive, 14, ITALY
e-mail: ballico@science.unitn.it

Abstract.Let , , be the order Veronese embedding of , the tangent developable of and the -secant variety of , i.e. the closure in of the union of all -linear spaces spanned by points of . has expected dimension . Catalisano, Geramita and Gimigliano conjectured that has always the expected dimension, except when , or and . In this paper we prove their conjecture when and , , and an asympotic case of the conjecture for all .