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

In this paper we study Weil-Petersson volumes of the moduli spaces of conicalhyperbolic surfaces. The moduli spaces are parametrised by their cone angleswhich naturally live inside Hassett's space of stability conditions on nodalcurves. Such stability conditions produce weighted pointed stable curves whichdefine compactifications of the moduli space of curves generalising theDeligne-Mumford compactification. The space of stability conditions decomposeinto chambers separated by walls. We assign to each chamber a polynomialcorresponding to the Weil-Petersson volume of a moduli space of conicalhyperbolic surfaces. The chambers are naturally partially ordered and themaximal chamber is assigned Mirzakhani's polynomial. We calculate wall-crossingpolynomials, which relates the polynomial on any chamber to Mirzakhani'spolynomial via wall-crossings, and we show how to apply this in particularcases. Since the polynomials are volumes, they have nice properties such aspositivity, continuity across walls, and vanishing in certain limits.

Weil-Petersson volumes, stability conditions and wall-crossing