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arXiv · 2008.09627

Chilean configuration of conics, lines and points

Igor Dolgachev·Antonio Laface·Ulf Persson·Giancarlo Urzúa
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Abstract

Using the theory of rational elliptic fibrations, we construct and discuss a one parameter family of configurations of $12$ conics and $9$ points in the projective plane that realizes an abstract configuration $(12_6,9_8)$. This is analogous to the famous Hesse configuration of $12$ lines and $9$ points forming an abstract configuration $(12_3,9_4)$. We also show that any Halphen elliptic fibration of index $2$ with four triangular singular fibers arises from such configuration of conics.

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Igor Dolgachev, Antonio Laface, Ulf Persson, Giancarlo Urzúa. 2020-08-21. Chilean configuration of conics, lines and points. https://arxiv.org/abs/2008.09627

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