Saturated orbit closures in the Hodge bundle

Abstract

We give a new proof of the classification of ${\mathrm{GL}}^{+}(2,\mathbb{R})$-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 ${\mathrm{GL}}^{+}(2,\mathbb{R})$-orbit closures using deformations of flat pairs of pants.

arXiv comment19 pages, 1 additional result, comments welcome