Toward a classification of tropical complete intersection number one

By bridging two classification results – the Esterov–Gusev classification of tuples of lattice polytopes of mixed volume one, and Fink’s characterization of Bergman fans – we formulate a classification conjecture describing when the stable intersection of a tropical fan F with the tropicalization Trop(X) of a subvariety of T^n is a reduced point. Our main results establish this conjecture in three fundamental cases – unmixed sequences, hypersurface complete-intersection cycles, and tropical 2-cycles – and develop several tools intended for the general case.