IJPAM: Volume 85, No. 5 (2013)

?REDUCIBLE CURVES AND THEIR ASSOCIATED RANK:
TWO EXTREMAL BEHAVIORS

E. Ballico
Department of Mathematics
University of Trento
38 123 Povo (Trento) - Via Sommarive, 14, ITALY


Abstract. Let Y ⊂ Pn be a reduced curve with < Y > = Pn, where < > denotes the linear span. For each P ∈ Pn the Y-rank rY(P) is the minimal cardinality of S ⊂ Y such that P ∈ < S >. Here we study two extremal behaviors: `` existence of P with rY(P)=n '' or ``  rY(P) ≤ ⌈ (n+1)/2 ⌉ for all P ∈ Pn ''.

Received: March 29, 2013

AMS Subject Classification: 14H99, 14N05

Key Words and Phrases: X-rank, reducible curve, union of lines

Download paper from here.


DOI: 10.12732/ijpam.v85i5.10 How to cite this paper?
Source: International Journal of Pure and Applied Mathematics
ISSN printed version: 1311-8080
ISSN on-line version: 1314-3395
Year: 2013
Volume: 85
Issue: 5