The equations of tensor train varieties

Tensor train varieties are parametrized projective varieties used to approximate the solutions to the electronic Schroedinger equation in second quantization. In particular, Rayleigh-Ritz optimization on these varieties plays a prominent role. This talk will present the equations of the defining ideal of any tensor train variety. They consist of minors of particular flattenings of the underlying tensors and these equations were conjectured by Sturmfels in an unpublished note. The proof uses the description of the ideal of the general Markov model on trees by Draisma and Kuttler.