English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

A meromorphic quadratic differential on a compact Riemann surface defines acomplex projective structure away from the poles via the Schwarzian equation.In this article we first prove the analogue of Thurston's Grafting Theorem forthe space of such structures with signings at regular singularities. Thisextends previous work of Gupta-Mj which only considered irregularsingularities. We also define a framed monodromy map from the signed spaceextending work of Allegretti-Bridgeland, and we characterize thePSL(2,C)-representations that arise as holonomy, generalizing results ofGupta-Mj and Faraco-Gupta. As an application of our Grafting Theorem, we alsoshow that the monodromy map to the moduli space of framed representations (asintroduced by Fock-Goncharov) is a local biholomorphism, proving a conjecturedanalogue of a result of Hejhal.

Meromorphic Projective Structures: Signed Spaces, Grafting and Monodromy