Regular and superabundant tropical curves

From CRCG-Wiki

Regular and superabundant tropical curves (Grigory Mikhalkin)

A tropical morphism from a (tropical) curve to a (tropical) manifold is called regular if its deformations are unobstructed, i.e. their dimension coincides with the one predicted by the Riemann-Roch formula. My recent theorem asserts that any regular curve is realizable, i.e. can be obtained as a degeneration limit of a classical 1-parametric family as long as the target is a smooth projective complete intersection. Realizability of superabundant curves is more delicate question -- there are examples of non-realizable as well as examples of realizable curves. The talk will review the current state of the realizability problem for superabundant curves and will contain many examples.