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Flex Curves and their Applications

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Abstract

In this paper, we define the notion of the flex curve F (ℙ)(f; P) at a nonsingular point P of a plane curve Ca. We construct interesting plane curves using a cyclic covering transform, branched along F (ℙ)(f; P). As an application, we show the moduli space of projective curves of degree 12 with 27 cusps has at least three irreducible components. Simultaneously, we give an example of Alexander-equivalent Zariski pair of irreducible curves.

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  1. Department of Mathematics, Tokyo Metropolitan University, Minami-Ohsawa, Hachioji-shi, Tokyo, 192-03, Japan

    Mutsuo Oka

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  1. Mutsuo Oka
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Oka, M. Flex Curves and their Applications. Geometriae Dedicata 75, 67–100 (1999). https://doi.org/10.1023/A:1005004123844

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