k-leaky double Hurwitz descendants
arxiv(2024)
摘要
We define a new class of enumerative invariants called k-leaky double
Hurwitz descendants, generalizing both descendant integrals of double
ramification cycles and the k-leaky double Hurwitz numbers introduced in
previous work of Cavalieri, Markwig and Ranganathan. These numbers are defined
as intersection numbers of the logarithmic DR cycle against ψ-classes and
logarithmic classes coming from piecewise polynomials encoding fixed branch
point conditions. We give a tropical graph sum formula for these new
invariants, allowing us to show their piecewise polynomiality and a
wall-crossing formula in genus zero. We also prove that in genus zero the
invariants are always non-negative and give a complete classification of the
cases where they vanish.
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