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arXiv · 1411.2648

On the Sylvester-Gallai theorem for conics

Adam Czaplinski·Marcin Dumnicki·Lucja Farnik·Janusz Gwozdziewicz·Magdalena Lampa-Baczynska·Grzegorz Malara·Tomasz Szemberg·Justyna Szpond·Halszka Tutaj-Gasinska
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Abstract

In the present note we give a new proof of a result due to Wiseman and Wilson 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. Specifically, we use Cremona transformation of the projective plane and Hirzebruch inequality.

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Adam Czaplinski, Marcin Dumnicki, Lucja Farnik, Janusz Gwozdziewicz, Magdalena Lampa-Baczynska, Grzegorz Malara, Tomasz Szemberg, Justyna Szpond, Halszka Tutaj-Gasinska. 2014-11-10. On the Sylvester-Gallai theorem for conics. https://doi.org/10.4171/rsmup%2F136-13

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