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TANGENT-FILLING PLANE CURVES OVER FINITE FIELDS

Part of: Arithmetic problems. Diophantine geometry Arithmetic algebraic geometry Projective and enumerative geometry Curves

Published online by Cambridge University Press:  02 May 2023

SHAMIL ASGARLI Open the ORCID record for SHAMIL ASGARLI [Opens in a new window]  and
DRAGOS GHIOCA Open the ORCID record for DRAGOS GHIOCA [Opens in a new window]
SHAMIL ASGARLI
Affiliation:
Department of Mathematics and Computer Science, Santa Clara University, 500 El Camino Real, Santa Clara, CA 95053, USA e-mail: sasgarli@scu.edu
DRAGOS GHIOCA*
Affiliation:
Department of Mathematics, University of British Columbia, Vancouver BC V6T 1Z2, Canada
*
e-mail: dghioca@math.ubc.ca
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Abstract

We study plane curves over finite fields whose tangent lines at smooth $\mathbb {F}_q$-points together cover all the points of $\mathbb {P}^2(\mathbb {F}_q)$.

Keywords

tangent-fillingplane curvesfinite fields

MSC classification

Primary: 14H50: Plane and space curves
Secondary: 11G20: Curves over finite and local fields 14G15: Finite ground fields 14N05: Projective techniques

Information

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 109 , Issue 2 , April 2024 , pp. 301 - 315
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Copyright
© The Author(s), 2023. Published by Cambridge University Press on behalf of Australian Mathematical Publishing Association Inc.

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