Sorbonne Université CNRS Paris Diderot

Géométrie énumérative

Welschinger weights and Segre indices for real lines on real hypersurfaces

Sergey Finashin - Middle East Technical University, Ankara

vendredi 25 janvier 2019 à 10:30
Jussieu, salle 15-16-413

In a joint work with V.Kharlamov, we explained how one may count real lines on real hypersurfaces (when their number is generically finite) with signs, so that the sum is independent of the choice of a hypersurfaces. These signs were assumed conjecturally to be equal to some multidimensional version of Welschinger weights. After elaborating this version of the weights, we proved this conjecture. We developed also a more geometric way of calculation : using the idea of Segre, who introduced two species of real lines on a cubic surface : hyperbolic and elliptic.

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