Linear General Position (i.e. Arcs) for Zero-Dimensional Schemes Over a Finite Field

Authors

  • Edoardo Ballico Department of Mathematics, University of Trento, 38123 Povo (TN), Italy

DOI:

https://doi.org/10.37256/cm.232021864

Keywords:

arcs, zero-dimensional scheme, linear general position sets

Abstract

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.

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Published

2021-08-10

How to Cite

1.
Ballico E. Linear General Position (i.e. Arcs) for Zero-Dimensional Schemes Over a Finite Field. Contemp. Math. [Internet]. 2021 Aug. 10 [cited 2024 May 20];2(3):231-8. Available from: https://ojs.wiserpub.com/index.php/CM/article/view/864