Toward a classification of tropical complete intersection number one

Abstract

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.