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 R5 given by two quadratic forms in three variables. Together with previous work by Demeter, Guo, and Shi in the non-degenerate case, this pro-vides a classification of decoupling inequalities for pairs of quadratic forms in three variables.