k-nets embedded in a projective plane over a field

Author(s)

Korchmaros, Gabor ^[1] ; Nagy, Gabor P. ^[2] ; Pace, Nicola ^[3]

Affiliation

^[1] Univ Basilicata Contrada Macchia Romana, Dipartimento Matemat & Informat, I-85100 Potenza - Italy

^[2] Univ Szeged, Bolyai Inst, H-6725 Szeged - Hungary

^[3] Univ Sao Paulo, Inst Ciencias Matemat & Comp, BR-13560970 Sao Carlos, SP - Brazil

• Document type: Journal article
• Source: COMBINATORICA; v. 35, n. 1, p. 63-74, FEB 2015.
• Web of Science Citations: 4

Abstract

We investigate k-nets with ka parts per thousand yen4 embedded in the projective plane PG(2,) defined over a field ; they are line configurations in PG(2,) consisting of k pairwise disjoint line-sets, called components, such that any two lines from distinct families are concurrent with exactly one line from each component. The size of each component of a k-net is the same, the order of the k-net. If has zero characteristic, no embedded k-net for ka parts per thousand yen5 exists; see {[}11,14]. Here we prove that this holds true in positive characteristic p as long as p is sufficiently large compared with the order of the k-net. Our approach, different from that used in {[}11,14], also provides a new proof in characteristic zero. (AU)

• FAPESP's process: 12/03526-0 - Finite geometry, Algebraic curves and Applications to Coding Theory
• Grantee: Nicola Pace
• Support Opportunities: Scholarships in Brazil - Post-Doctoral