Global geometry on moduli of local systems for surfaces with boundary

Abstract

We show that every coarse moduli space, parametrizing complex special linear rank two local systems with fixed boundary traces on a surface with nonempty boundary, is log Calabi-Yau in that it has a normal projective compactification with trivial log canonical divisor. We connect this to a novel symmetry of generating series for counts of essential multicurves on the surface.

41 pages, 3 figures; accepted for publication in Compositio Mathematica

References in corpus (2)

• The dual complex of Calabi--Yau pairs
• Conic bundles that are not birational to numerical Calabi--Yau pairs

Cited by in corpus (3)

• Surface group representations in ${\mathrm{SL}}_2(\mathbb{C})$ with finite mapping class orbits
• Cell decomposition and dual boundary complexes of character varieties
• Arithmetic of curves on moduli of local systems