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Global geometry on moduli of local systems for surfaces with boundary

Part of: Surfaces and higher-dimensional varieties Low-dimensional topology

Published online by Cambridge University Press:  01 October 2020

Junho Peter Whang
Junho Peter Whang*
Affiliation:
Department of Mathematics, Massachusetts Institute of Technology, Simons Building Room 2-238A, 77 Massachusetts Avenue, Cambridge, MA 02139-4307, USA jwhang@mit.edu
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Abstract

We show that every coarse moduli space, parametrizing complex special linear rank-2 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.

Keywords

character varietycompactificationlog Calabi–Yausurfacemulticurve

MSC classification

Primary: 14J32: Calabi-Yau manifolds
Secondary: 57M05: Fundamental group, presentations, free differential calculus
Type
Research Article
Information
Compositio Mathematica , Volume 156 , Issue 8 , August 2020 , pp. 1517 - 1559
Copyright
Copyright © The Author(s) 2020

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