$k$-leaky double Hurwitz descendants
Fuente:
arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2024
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| Acceso en línea: | |
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| _version_ | 1866910411842912256 |
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| author | Cavalieri, Renzo Markwig, Hannah Schmitt, Johannes |
| author_facet | Cavalieri, Renzo Markwig, Hannah Schmitt, Johannes |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_10168 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | $k$-leaky double Hurwitz descendants Cavalieri, Renzo Markwig, Hannah Schmitt, Johannes Algebraic Geometry Combinatorics 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. |
| title | $k$-leaky double Hurwitz descendants |
| topic | Algebraic Geometry Combinatorics |
| url | https://arxiv.org/abs/2404.10168 |