JournalsrsmupVol. 136pp. 191–203

On the Sylvester–Gallai theorem for conics

  • Adam Czapliński

    Johannes Gutenberg-Universität Mainz, Germany
  • Marcin Dumnicki

    Jagiellonian University, Kraków, Poland
  • Łucja Farnik

    Jagiellonian University, Kraków, Poland
  • Janusz Gwoździewicz

    Pedagogical University of Cracow, Kraków, Poland
  • Magdalena Lampa-Baczyńska

    Pedagogical University of Cracow, Kraków, Poland
  • Grzegorz Malara

    Pedagogical University of Cracow, Kraków, Poland
  • Tomasz Szemberg

    Krakow Pedagogical Academy, Kraków, Poland
  • Justyna Szpond

    Pedagogical University of Cracow, Kraków, Poland
  • Halszka Tutaj-Gasińska

    Jagiellonian University, Kraków, Poland
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Abstract

In the present note we give a new proof of a result due to Wiseman and Wilson [13] which establishes an analogue of the Sylvester–Gallai theorem valid for curves of degree two. The main ingredients of the proof come from algebraic geometry. Specically, we use Cremona transformation of the projective plane and Hirzebruch inequality (1).

Cite this article

Adam Czapliński, Marcin Dumnicki, Łucja Farnik, Janusz Gwoździewicz, Magdalena Lampa-Baczyńska, Grzegorz Malara, Tomasz Szemberg, Justyna Szpond, Halszka Tutaj-Gasińska, On the Sylvester–Gallai theorem for conics. Rend. Sem. Mat. Univ. Padova 136 (2016), pp. 191–203

DOI 10.4171/RSMUP/136-13