Chilean configuration of conics, lines and points
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Date
2022
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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.