The coerciveness and generalised Monge-Ampère equations

In this paper, we prove the equivalence between coerciveness and the existence of a solution to the generalised Monge-Ampère equations for right-Noetherian polynomials satisfying several assumptions. This includes the case of strictly interlacing polynomials. In particular, we have generalised Chu-Lee’s result to supercritical but not hypercritical LYZ equations.