A tropical curve is superabundant if its space of deformation
has dimension greater than the expected one. In this case the tropical
curve may or may not be approximable by complex algebraic curves, and no
necessary and sufficient criterion to make the distinction is known at
the moment.
In this talk I will discuss some necessary or sufficient conditions for
a tropical curve to be approximable. In the case of tropical morphisms
from a curve to a curve, this leads to a combinatorial "if and only if"
criterion.
This work has been done jointly with Grigory Mikhalkin, and extends
earlier results by G. Mikhalkin, and by David Speyer.

Lecture #13937

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