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International conference "Birational and affine geometry"
April 25, 2012 16:00–16:50, Moscow, Steklov Mathematical Institute of RAS
 


Plane cubics and their flex lines

D. Testa

University of Warwick, Mathematics Institute
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D. Testa
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Abstract: Special tangent lines to plane curves have been studied intensively: flexes of plane cubics simplify the construction of the group law on the cubic, bitangents to plane quartics can be used to find the lines on a smooth cubic surface, flexes and bitangents appear in the Plücker formulas, and so on. For example, a smooth plane cubic has nine flex lines (and no bitangents).
This talk is based on joint work with M. Pacini: we show how to reconstruct a smooth plane cubic from its nine flex lines. The reconstruction procedure works over any field of characteristic different from three and is completely uniform with a unique exception.

Language: English

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