Decoupling for two quadratic forms in three variables: a complete characterization

Abstract

We prove sharp decoupling inequalities for all degenerate surfaces of codimension two in ${\mathbb{R}}^5$ given by two quadratic forms in three variables. Together with previous work by Demeter, Guo, and Shi in the non-degenerate case, this provides a classification of decoupling inequalities for pairs of quadratic forms in three variables.