Polynomiality of the double ramification cycle
Fuente:
arXiv
Saved in:
| Main Author: | |
|---|---|
| Format: | Preprint |
| Published: |
2024
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866929230014578688 |
|---|---|
| author | Spelier, Pim |
| author_facet | Spelier, Pim |
| contents | Let $A = (a_1,\dots,a_n)\in \mathbb{Z}^n$ be a sequence with sum $k(2g-2+n)$. The double ramification cycle $\mathsf{DR}_g(A) \in \mathsf{CH}^g(\bar{\mathcal{M}}_{g,n})$ is the virtual class of the locus of curves $(C,p_1,\dots,p_n)$ where the line bundle $(ω_C^{\log})^{-k}\left(\sum a_i p_i\right)$ is trivial. Although there has long been a formula for $\mathsf{DR}_g(A)$ [JPPZ17], the exact dependence on $A$ was unknown for a long time, though it was conjectured to be polynomial in $A$. A proof was announced in [JPPZ17], and Pixton gave a proof incorporating ideas of Zagier in [Pix23]. Here we present an alternative proof of the polynomiality of the double ramification cycle. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_17421 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Polynomiality of the double ramification cycle Spelier, Pim Algebraic Geometry Let $A = (a_1,\dots,a_n)\in \mathbb{Z}^n$ be a sequence with sum $k(2g-2+n)$. The double ramification cycle $\mathsf{DR}_g(A) \in \mathsf{CH}^g(\bar{\mathcal{M}}_{g,n})$ is the virtual class of the locus of curves $(C,p_1,\dots,p_n)$ where the line bundle $(ω_C^{\log})^{-k}\left(\sum a_i p_i\right)$ is trivial. Although there has long been a formula for $\mathsf{DR}_g(A)$ [JPPZ17], the exact dependence on $A$ was unknown for a long time, though it was conjectured to be polynomial in $A$. A proof was announced in [JPPZ17], and Pixton gave a proof incorporating ideas of Zagier in [Pix23]. Here we present an alternative proof of the polynomiality of the double ramification cycle. |
| title | Polynomiality of the double ramification cycle |
| topic | Algebraic Geometry |
| url | https://arxiv.org/abs/2401.17421 |