Saturated Orbit Closures in the Hodge Bundle

Abstract

We give a new proof of the classification of $\operatorname {GL}^{+}(2,{\mathbb {R}})$-orbit closures that are saturated for the absolute period foliation of the Hodge bundle. As a consequence, we obtain a short proof of the classification of closures of leaves of the absolute period foliation of the Hodge bundle. Our approach is based on a method for classifying $\operatorname {GL}^{+}(2,{\mathbb {R}})$-orbit closures using deformations of flat pairs of pants.