Hurwitz correspondences on compactifications of M_{0,N}
-- Rohini Ramadas, October 30, 2015

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Hurwitz correspondences are multivalued maps from M_{0,N1} to
M_{0,N2} that descend from holomorphic maps on Teichmuller space. We
consider the dynamics of Hurwitz self-correspondences and ask: On
which compactifications of M_{0,N} should they be studied? We compare
a Hurwitz self-correspondence H on two different compactifications:
the stable curves compactification \overline{M}_{0,N} and an alternate
weighted stable curves compactification. We use this comparison to
show that, for k > (dim M_{0,N} - 1)/2, the k-th dynamical degree of H
is the absolute value of the largest eigenvalue of the pushforward map
induced by H on a comparatively small quotient of H^{2k}(M_{0,N}).