On the Sylvester–Gallai theorem for conics
Adam Czapliński
Johannes Gutenberg-Universität Mainz, GermanyMarcin Dumnicki
Jagiellonian University, Kraków, PolandŁucja Farnik
Jagiellonian University, Kraków, PolandJanusz Gwoździewicz
Pedagogical University of Cracow, Kraków, PolandMagdalena Lampa-Baczyńska
Pedagogical University of Cracow, Kraków, PolandGrzegorz Malara
Pedagogical University of Cracow, Kraków, PolandTomasz Szemberg
Krakow Pedagogical Academy, Kraków, PolandJustyna Szpond
Pedagogical University of Cracow, Kraków, PolandHalszka Tutaj-Gasińska
Jagiellonian University, Kraków, Poland
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. Speci cally, 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