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Quasimap wall-crossings and mirror symmetry

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Abstract

We state a wall-crossing formula for the virtual classes of \({\varepsilon }\)-stable quasimaps to GIT quotients and prove it for complete intersections in projective space, with no positivity restrictions on their first Chern class. As a consequence, the wall-crossing formula relating the genus \(g\) descendant Gromov-Witten potential and the genus \(g\)\({\varepsilon }\)-quasimap descendant potential is established. For the quintic threefold, our results may be interpreted as giving a rigorous and geometric interpretation of the holomorphic limit of the BCOV \(B\)-model partition function of the mirror family.

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Authors and Affiliations

  1. School of Mathematics, University of Minnesota, 206 Church St. SE, Minneapolis, MN, 55455, USA

    Ionuţ Ciocan-Fontanine

  2. School of Mathematics, Korea Institute for Advanced Study, 85 Hoegiro, Dongdaemun-gu, Seoul, 02455, Korea

    Ionuţ Ciocan-Fontanine & Bumsig Kim

Authors
  1. Ionuţ Ciocan-Fontanine
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  2. Bumsig Kim
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Correspondence to Bumsig Kim.

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Ciocan-Fontanine, I., Kim, B. Quasimap wall-crossings and mirror symmetry. Publ.math.IHES 131, 201–260 (2020). https://doi.org/10.1007/s10240-020-00114-0

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  • DOI: https://doi.org/10.1007/s10240-020-00114-0

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