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.
Highlights
The equality of the two expressions on the right-hand side is a non-trivial claim about intersection numbers on P Mg,n(μ)
In order to prove it, we show that both sides of Eq (2) satisfy the same recursion formula
The recursion formula is expressed via an operator acting on Bloch and Okounkov’s algebra of shifted symmetric functions
Summary
We recall the definition of the moduli space of admissible covers of [27] as a compactification of the classical Hurwitz space (see [28]), and prove formulas to compute recursively intersection numbers of ψ-classes on these moduli spaces. Along the way we introduce basic notions on stable graphs and level functions
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