Masur–Veech volumes and intersection theory on moduli spaces of Abelian differentials
Dawei Chen, Martin Möller, Adrien Sauvaget, Don Zagier
Abstract
Abstract We show that the Masur–Veech volumes and area Siegel–Veech constants can be obtained using intersection theory on strata of Abelian differentials with prescribed orders of zeros. As applications, we evaluate their large genus limits and compute the saddle connection Siegel–Veech constants for all strata. We also show that the same results hold for the spin and hyperelliptic components of the strata.
Topics & Concepts
MathematicsAbelian groupModuli spaceIntersection (aeronautics)GenusPure mathematicsIntersection theoryModuliConnection (principal bundle)CombinatoricsMathematical analysisGeometryGeographyBotanyPhysicsDifferential equationBiologyOrdinary differential equationDifferential algebraic equationCartographyQuantum mechanicsMathematical Dynamics and FractalsAdvanced Topology and Set Theoryadvanced mathematical theories