k-nets embedded in a projective plane over a field View Full Text


Ontology type: schema:ScholarlyArticle      Open Access: True


Article Info

DATE

2015-02

AUTHORS

Gábor Korchmáros, Gábor P. Nagy, Nicola Pace

ABSTRACT

We investigate k-nets with k≥4 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 k≥5 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. More... »

PAGES

63-74

References to SciGraph publications

Identifiers

URI

http://scigraph.springernature.com/pub.10.1007/s00493-011-3055-z

DOI

http://dx.doi.org/10.1007/s00493-011-3055-z

DIMENSIONS

https://app.dimensions.ai/details/publication/pub.1022938259


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