Abstract
We prove that there are no Shimura–Teichmuller curves generated by genus five translation surfaces, thereby completing the classification of Shimura–Teichmuller curves in general. This was conjectured by Moller in his original work introducing Shimura–Teichmuller curves. Moreover, the property of being a Shimura–Teichmuller curve is equivalent to having completely degenerate Kontsevich–Zorich spectrum. The main new ingredient comes from the work of Hu and the second named author, which facilitates calculations of higher order terms in the period matrix with respect to plumbing coordinates. A large computer search is implemented to exclude the remaining cases, which must be performed in a very specific way to be computationally feasible.
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
