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Tropical double ramification loci

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 نشر من قبل Dmitry Zakharov
 تاريخ النشر 2019
  مجال البحث
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Motivated by the realizability problem for principal tropical divisors with a fixed ramification profile, we explore the tropical geometry of the double ramification locus in $mathcal{M}_{g,n}$.There are two ways to define a tropical analogue of the double ramification locus: one as a locus of principal divisors, the other as a locus of finite effective ramified covers of a tree. We show that both loci admit a structure of a generalized cone complex in $M_{g,n}^{trop}$, with the latter contained in the former. We prove that the locus of principal divisors has cones of codimension zero in $M_{g,n}^{trop}$, while the locus of ramified covers has the expected codimension $g$. This solves the deformation-theoretic part of the realizability problem for principal divisors, reducing it to the so-called Hurwitz existence problem for covers of a fixed ramification type.



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