On the solvability of operators with multiple characteristics

We study the solvability of partial differential operators with multiple characteristics, whose characteristic varieties have singularities outside the zero-section of the cotangent bundle. By making use of the theory of bimicrolocalization, we prove the solvability for a class of operators in the space of Sato's hyperfunctions. This result generalizes the classical results due to Bony-Schapira and Kashiwara-Kawai etc. To obtain it, we also discuss the solvability for systems of partial differential equations.