Shimura- and Teichmueller curves

Details Shimura- and Teichmueller curves Shimura- and Teichmueller curves

2005-01-20

arxiv.org/abs/math/0501333v2

Mathematics

Algebraic Geometry

Major revision. Main result weakened concerning the case of genus 5 curves. One missing case added in genus 4. Application to

Scientific paper

We classify curves in the moduli space of curves that are both Shimura- and Teichmueller curves: Except for the moduli space of genus one curves there is only a single such curve. We start with a Hodge-theoretic description of Shimura curves and of Teichmueller curves that reveals similarities and differences of the two classes of curves. The proof of the classification relies on the geometry of square-tiled coverings and on estimating the numerical invariants of these particular fibered surfaces. Finally we translate our main result into a classification of Teichmueller curves with totally degenerate Lyapunov spectrum.

Affiliated with

Also associated with

No associations

Rating

Shimura- and Teichmueller curves does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Shimura- and Teichmueller curves, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Shimura- and Teichmueller curves will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-641645