# IJPAM: Volume 81, No. 6 (2012)

ON THE CONNECTED RANK FOR PROJECTIVE VARIETIES

E. Ballico
Department of Mathematics
University of Trento
38 123 Povo (Trento) - Via Sommarive, 14, ITALY
e-mail: ballico@science.unitn.it

Abstract. We start the discussion of the following query. Let be an integral and non-degenerate curve. For each let (resp. , resp. ) be the minimal degree of a zero-dimensional (resp. zero-dimensional and connected, resp. zero-dimensional connected and curvilinear) scheme such that , where denote the linear span. Compute the maximal integer and when is arbitrary (resp. general) in .

AMS Subject Classification: 14N10, 14H45

Key Words and Phrases: symmetric tensor rank, connected rank, curvilinear scheme, cactus rank