TANGENT-FILLING PLANE CURVES OVER FINITE FIELDS

<jats:p>We study plane curves over finite fields whose tangent lines at smooth <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" mime-subtype="png" xlink:href="S0004972723000382_inline1.png" /> <jats:tex-math> $\mathbb {F}_q$ </jats:tex-math> </jats:alternatives> </jats:inline-formula>-points together cover all the points of <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" mime-subtype="png" xlink:href="S0004972723000382_inline2.png" /> <jats:tex-math> $\mathbb {P}^2(\mathbb {F}_q)$ </jats:tex-math> </jats:alternatives> </jats:inline-formula>.</jats:p>

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