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arXiv · 2609.12213

Siebert's formula for virtual pullbacks

Xuanchun Lu·Rachel Webb
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Abstract

For a DM-type morphism of algebraic stacks $f \colon X \to Y$ with a relative perfect obstruction theory $\mathbb{E} \to \mathbb{L}_{X/Y}$ having a global resolution, we give a formula for the induced virtual pullback in terms of $\mathbb{E}$ and $f$. We apply our formula to prove functoriality properties of the virtual fundamental class in Gromov-Witten theory.

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Xuanchun Lu, Rachel Webb. 2026-09-10. Siebert's formula for virtual pullbacks. https://arxiv.org/abs/2609.12213

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