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<p>We construct an <i>I</i>-function for toric bundles obtained as a fiberwise GIT quotient of a (not necessarily split) vector bundle. This is a generalization of Brown’s <i>I</i>-function for split toric bundles (Brown in Int Math Res Not IMRN 19:5437–5482, 2014) and the <i>I</i>-function for non-split projective bundles (Iritani and Koto in <a href="http://arxiv.org/abs/2307.03696">arXiv:2307.03696</a> [math.AG], 2023). In order to prove the mirror theorem, we establish a characterization of points on the Givental Lagrangian cones of toric bundles and prove a mirror theorem for the twisted Gromov–Witten theory of a fiber product of projective bundles. The former result generalizes Brown’s characterization for split toric bundles [<CitationRef CitationID="CR6">6</CitationRef>] to the non-split case.</p>

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A mirror theorem for non-split toric bundles

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  • 发表日期：

    2025年11月5日

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  • Yuki Koto

摘要

We construct an I-function for toric bundles obtained as a fiberwise GIT quotient of a (not necessarily split) vector bundle. This is a generalization of Brown’s I-function for split toric bundles (Brown in Int Math Res Not IMRN 19:5437–5482, 2014) and the I-function for non-split projective bundles (Iritani and Koto in arXiv:2307.03696 [math.AG], 2023). In order to prove the mirror theorem, we establish a characterization of points on the Givental Lagrangian cones of toric bundles and prove a mirror theorem for the twisted Gromov–Witten theory of a fiber product of projective bundles. The former result generalizes Brown’s characterization for split toric bundles [6] to the non-split case.