On the Sylvester–Gallai theorem for conics
Czapliński, Adam1 ; Dumnicki, Marcin2 ; Farnik, Łucja2 ; Gwoździewicz, Janusz3 ; Lampa-Baczyńska, Magdalena3 ; Malara, Grzegorz3 ; Szemberg, Tomasz4 ; Szpond, Justyna3 ; Tutaj-Gasińska, Halszka2
1 Johannes Gutenberg-Universität Mainz, MAINZ, GERMANY
2 Jagiellonian University, KRAKÓW, POLAND
3 Pedagogical University of Cracow, KRAKÓW, POLAND
4 Krakow Pedagogical Academy, KRAKÓW, POLAND
Rendiconti del Seminario Matematico della Università di Padova, Tome 136 (2016), pp. 191-203.

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).

DOI : 10.4171/RSMUP/136-13
Classification : 52, 05, 14
Mots clés : Arrangements of subvarieties, combinatorial arrangements, Sylvester–Gallai problem, Cremona transformation, Hirzebruch inequality, interpolation problem
Czapliński, Adam 1 ; Dumnicki, Marcin 2 ; Farnik, Łucja 2 ; Gwoździewicz, Janusz 3 ; Lampa-Baczyńska, Magdalena 3 ; Malara, Grzegorz 3 ; Szemberg, Tomasz 4 ; Szpond, Justyna 3 ; Tutaj-Gasińska, Halszka 2

1 Johannes Gutenberg-Universität Mainz, MAINZ, GERMANY
2 Jagiellonian University, KRAKÓW, POLAND
3 Pedagogical University of Cracow, KRAKÓW, POLAND
4 Krakow Pedagogical Academy, KRAKÓW, POLAND 
@article{RSMUP_2016__136__191_0,
     author = {Czapli\'nski, Adam and Dumnicki, Marcin and Farnik, {\L}ucja and Gwo\'zdziewicz, Janusz and Lampa-Baczy\'nska, Magdalena and Malara, Grzegorz and Szemberg, Tomasz and Szpond, Justyna and Tutaj-Gasi\'nska, Halszka},
     title = {On the {Sylvester{\textendash}Gallai} theorem for conics},
     journal = {Rendiconti del Seminario Matematico della Universit\`a di Padova},
     pages = {191--203},
     publisher = {European Mathematical Society Publishing House},
     address = {Zuerich, Switzerland},
     volume = {136},
     year = {2016},
     doi = {10.4171/RSMUP/136-13},
     url = {http://www.numdam.org/articles/10.4171/RSMUP/136-13/}
}
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Czapliński, Adam; Dumnicki, Marcin; Farnik, Łucja; Gwoździewicz, Janusz; Lampa-Baczyńska, Magdalena; Malara, Grzegorz; Szemberg, Tomasz; Szpond, Justyna; Tutaj-Gasińska, Halszka. On the Sylvester–Gallai theorem for conics. Rendiconti del Seminario Matematico della Università di Padova, Tome 136 (2016), pp. 191-203. doi : 10.4171/RSMUP/136-13. http://www.numdam.org/articles/10.4171/RSMUP/136-13/

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