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arXiv · 2508.15770

Quantum cohomology of variations of GIT quotients and flips

Zhaoxing Gu·Song Yu·Tony Yue YU
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Abstract

We prove a decomposition theorem for the quantum cohomology of variations of GIT quotients. More precisely, for any reductive group $G$ and a simple $G$-VGIT wall-crossing $X_- \dashrightarrow X_+$ with a wall $S$, we show that the quantum $D$-module of $X_-$ can be decomposed into a direct sum of that of $X_+$ and copies of that of $S$. As an application, we obtain a decomposition theorem for the quantum cohomology of local models of standard flips in birational geometry.

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Zhaoxing Gu, Song Yu, Tony Yue YU. 2025-08-21. Quantum cohomology of variations of GIT quotients and flips. https://arxiv.org/abs/2508.15770

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