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arXiv · 2504.09726

Splitting formulas for the logarithmic double ramification cycle

Pim Spelier
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Abstract

The logarithmic double ramification cycle is roughly a logarithmic Gromov--Witten invariant of $\mathbb{P}^1$. For classical Gromov--Witten invariants, formulas for the pullback along the gluing maps have been invaluable to the theory. For logarithmic Gromov--Witten invariants, such formulas have not yet been found. One issue is the fact that log stable maps cannot be glued. In this paper, we use the framework from [HS23] for gluing pierced log curves (a refinement of classical log curves) to give formulas for the pullback of the (log) (twisted) double ramification cycle along the loop gluing map.

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Pim Spelier. 2025-04-13. Splitting formulas for the logarithmic double ramification cycle. https://arxiv.org/abs/2504.09726

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