Enumeration of real curves interpolating a configuration of points

Erwan Brugallé
École Polytechnique

How many real algebraic curves of a given degree and genus interpolate a given configuration of points in the plane? This number heavily depends on the chosen configuration, and a complete answer to this question seems out of reach.
I will discuss some methods to construct configurations for which one can recover all interpolating real curves, allowing in particular their enumeration. In the case of rational curves, one deduces non-trivial lower bounds valid for any configuration, thanks to Welschinger invariants.

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