David Aulicino, Aaron Calderon, Carlos Matheus, Nick Salter, Martin Schmoll
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引用次数: 0
Abstract
We compute the asymptotic number of cylinders, weighted by their area to any
non-negative power, on any cyclic branched cover of any generic translation
surface in any stratum. Our formulas depend only on topological invariants of
the cover and number-theoretic properties of the degree: in particular, the
ratio of the related Siegel-Veech constants for the locus of covers and for the
base stratum component is independent of the number of branch values. One
surprising corollary is that this ratio for $area^3$ Siegel-Veech constants is
always equal to the reciprocal of the the degree of the cover. A key ingredient
is a classification of the connected components of certain loci of cyclic
branched covers.
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