Some examples of isotropic SL(2,R)-invariant subbundles of the Hodge bundle
Carlos Matheus, Gabriela Weitze-Schmithuesen
TL;DR
This paper constructs specific origamis (square-tiled surfaces) demonstrating non-trivial isotropic SL(2,R)-invariant subbundles in the Hodge bundle, answering a question by Eskin and Forni.
Contribution
It provides explicit examples of origamis with SL(2,R)-invariant subbundles, advancing understanding of the structure of Hodge bundles over moduli space orbits.
Findings
Existence of origamis with non-trivial isotropic SL(2,R)-invariant subbundles
Answers to a question by Eskin and Forni about Hodge bundle substructures
Concrete examples enriching the theory of SL(2,R)-orbit dynamics
Abstract
We construct some examples of origamis (square-tiled surfaces) such that the Hodge bundles over the corresponding SL(2,R)-orbits on the moduli space admit non-trivial isotropic SL(2,R)-invariant subbundles. This answers a question posed to the authors by A. Eskin and G. Forni.
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Taxonomy
TopicsAlgebraic Geometry and Number Theory · Advanced Algebra and Geometry · Geometry and complex manifolds