Novikov's four-jet characterization of Jacobians

Let a principally polarized indecomposable abelian variety be given, with its Kummer variety and associated theta functions. A family of flex lines has a fourth-order jet when its flex condition is specified to fourth order. Novikov's conjecture. The existence of a fourth-order jet of a family of flex lines of the Kummer variety characterizes Jacobians. Equivalently, a principally polarized indecomposable abelian variety is a Jacobian if and only if its associated theta functions satisfy the KP equation. This was conjectured by Novikov and proved by Shiota; the result gives a solution to the Schottky problem, with the KP equation being the first nontrivial equation in the KP hierarchy.