An analogue of the Torelli theorem for Kummer surfaces of Jacobians

In this paper we obtain algebraic criteria that isolate the class of Kummer surfaces of Jacobians of curves of genus 2 within the class of $K3$ surfaces. In addition, we prove analogues of Torelli's theorems for these surfaces and find a “standard” representation for them as a complete intersection of three quadrics in $\mathbf P^5$.