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).
Classification :
52, 05, 14
Mots-clés : Arrangements of subvarieties, combinatorial arrangements, Sylvester–Gallai problem, Cremona transformation, Hirzebruch inequality, interpolation problem
Mots-clés : Arrangements of subvarieties, combinatorial arrangements, Sylvester–Gallai problem, Cremona transformation, Hirzebruch inequality, interpolation problem
Affiliations des auteurs :
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
@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/} }
TY - JOUR AU - Czapliński, Adam AU - Dumnicki, Marcin AU - Farnik, Łucja AU - Gwoździewicz, Janusz AU - Lampa-Baczyńska, Magdalena AU - Malara, Grzegorz AU - Szemberg, Tomasz AU - Szpond, Justyna AU - Tutaj-Gasińska, Halszka TI - On the Sylvester–Gallai theorem for conics JO - Rendiconti del Seminario Matematico della Università di Padova PY - 2016 SP - 191 EP - 203 VL - 136 PB - European Mathematical Society Publishing House PP - Zuerich, Switzerland UR - http://www.numdam.org/articles/10.4171/RSMUP/136-13/ DO - 10.4171/RSMUP/136-13 ID - RSMUP_2016__136__191_0 ER -
%0 Journal Article %A Czapliński, Adam %A Dumnicki, Marcin %A Farnik, Łucja %A Gwoździewicz, Janusz %A Lampa-Baczyńska, Magdalena %A Malara, Grzegorz %A Szemberg, Tomasz %A Szpond, Justyna %A Tutaj-Gasińska, Halszka %T On the Sylvester–Gallai theorem for conics %J Rendiconti del Seminario Matematico della Università di Padova %D 2016 %P 191-203 %V 136 %I European Mathematical Society Publishing House %C Zuerich, Switzerland %U http://www.numdam.org/articles/10.4171/RSMUP/136-13/ %R 10.4171/RSMUP/136-13 %F RSMUP_2016__136__191_0
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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