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Peer-reviewedCC BYAlgebraic geometry

Polynomiality of the double ramification cycle

  • Pim Spelier
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Abstract

Let A = (a 1 , . . ., a n ) ∈ Z n be a sequence with sum k(2g-2+n).The double ramification cycle DR g (A) ∈ CH g M g,n is the virtual class of the locus of curves (C, p 1 , . . ., p n ) where the line bundle ω log C -k a i p i is trivial.Although there has long been a formula for DR g (A), the exact dependence on A was unknown for a long time, though it was conjectured to be polynomial in A. A proof was announced by Janda, Pandharipande, Pixton, and Zvonkine in 2017, and Pixton gave a proof incorporating ideas of Zagier in 2023.Here we present an alternative proof of the polynomiality of the double ramification cycle.

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Cite

BibTeXRIS
BibTeX
@article{spelier2026polynomiality,
  title = {{Polynomiality of the double ramification cycle}},
  author = {Pim Spelier},
  journal = {Algebraic geometry},
  year = {2026},
  month = jun,
  doi = {10.14231/ag-2026-017},
  url = {https://doi.org/10.14231/ag-2026-017},
  note = {CC BY},
}
RIS
TY  - JOUR
TI  - Polynomiality of the double ramification cycle
AU  - Pim Spelier
PY  - 2026
DA  - 2026/06/12
JO  - Algebraic geometry
DO  - 10.14231/ag-2026-017
UR  - https://doi.org/10.14231/ag-2026-017
AB  - Let A = (a 1 , . . ., a n ) ∈ Z n be a sequence with sum k(2g-2+n).The double ramification cycle DR g (A) ∈ CH g M g,n is the virtual class of the locus of curves (C, p 1 , . . ., p n ) where the line bundle ω log C -k a i p i is trivial.Although there has long been a formula for DR g (A), the exact dependence on A was unknown for a long time, though it was conjectured to be polynomial in A. A proof was announced by Janda, Pandharipande, Pixton, and Zvonkine in 2017, and Pixton gave a proof incorporating ideas of Zagier in 2023.Here we present an alternative proof of the polynomiality of the double ramification cycle.
SN  - 2214-2584
SN  - 2313-1691
ER  -