Global geometry on moduli of local systems for surfaces with boundary
Junho Peter Whang
Abstract
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.
Topics & Concepts
MathematicsModuliCompactification (mathematics)Boundary (topology)Pure mathematicsGeometrySurface (topology)Mathematical analysisModuli spaceModuli of algebraic curvesMirror symmetrySymmetry (geometry)Series (stratigraphy)Linear systemModular equationBoundary value problemSymmetry groupAlgebraic geometryFinitely-generated abelian groupAlgebra over a fieldAlgebraic Geometry and Number TheoryGeometry and complex manifoldsAdvanced Algebra and Geometry