The local-global property for bitangents of plane quartics

20 Apr 2020 Ishitsuka Yasuhiro Ito Tetsushi Ohshita Tatsuya Taniguchi Takashi Uchida Yukihiro

We study the arithmetic of bitangents of smooth quartics over global fields. With the aid of computer algebra systems and using Elsenhans--Jahnel's results on the inverse Galois problem for bitangents, we show that, over any global field of characteristic different from $2$, there exist smooth quartics which have bitangents over every local field, but do not have bitangents over the global field... (read more)

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Categories


  • NUMBER THEORY
  • ALGEBRAIC GEOMETRY