Open AccessLinear General Position (i.e. Arcs) for Zero-Dimensional Schemes Over a Finite Field
Author(s) -
Edoardo Ballico
Publication year - 2021
Publication title -
contemporary mathematics
Language(s) - English
Resource type - Journals
eISSN - 2705-1064
pISSN - 2705-1056
DOI - 10.37256/cm.232021864
Subject(s) - mathematics , zero (linguistics) , finite field , projective space , finite geometry , field (mathematics) , position (finance) , pure mathematics , type (biology) , space (punctuation) , mathematical analysis , projective plane , projective test , geometry , discrete mathematics , ecology , philosophy , linguistics , finance , economics , correlation , biology
We extend some of the usual notions of projective geometry over a finite field (arcs and caps) to the case of zero-dimensional schemes defined over a finite field Fq. In particular we prove that for our type of zero-dimensional arcs the maximum degree in any r-dimensional projective space is r(q + 1) and (if either r = 2 or q is odd) all the maximal cases are projectively equivalent and come from a rational normal curve.