I will explain an explicit weak solution to the Schottky problem. For any genus $g$, we wrote down a collection of polynomials in genus g theta constants, such that their common zero locus contains the locus of Jacobians of genus $g$ curves as an irreducible component. These polynomials arise by applying a specific Schottky-Jung proportionality to an explicit collection of quartic identities for genus $(g − 1)$ theta constant. ( joint work with H. Farkas and S. Grushevsky)
