We state a wall-crossing formula for the virtual classes of -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 descendant Gromov-Witten potential and the genus -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 -model partition function of the mirror family.
@article{PMIHES_2020__131__201_0,
author = {Ionu\c{t} Ciocan-Fontanine and Bumsig Kim},
title = {Quasimap wall-crossings and mirror symmetry},
journal = {Publications Math\'ematiques de l'IH\'ES},
pages = {201--260},
year = {2020},
publisher = {Springer Berlin Heidelberg},
address = {Berlin/Heidelberg},
volume = {131},
doi = {10.1007/s10240-020-00114-0},
zbl = {1475.14109},
language = {en},
url = {https://pmihes.centre-mersenne.org/articles/10.1007/s10240-020-00114-0/}
}
TY - JOUR AU - Ionuţ Ciocan-Fontanine AU - Bumsig Kim TI - Quasimap wall-crossings and mirror symmetry JO - Publications Mathématiques de l'IHÉS PY - 2020 SP - 201 EP - 260 VL - 131 PB - Springer Berlin Heidelberg PP - Berlin/Heidelberg UR - https://pmihes.centre-mersenne.org/articles/10.1007/s10240-020-00114-0/ DO - 10.1007/s10240-020-00114-0 LA - en ID - PMIHES_2020__131__201_0 ER -
%0 Journal Article %A Ionuţ Ciocan-Fontanine %A Bumsig Kim %T Quasimap wall-crossings and mirror symmetry %J Publications Mathématiques de l'IHÉS %D 2020 %P 201-260 %V 131 %I Springer Berlin Heidelberg %C Berlin/Heidelberg %U https://pmihes.centre-mersenne.org/articles/10.1007/s10240-020-00114-0/ %R 10.1007/s10240-020-00114-0 %G en %F PMIHES_2020__131__201_0
Ionuţ Ciocan-Fontanine; Bumsig Kim. Quasimap wall-crossings and mirror symmetry. Publications Mathématiques de l'IHÉS, Volume 131 (2020), pp. 201-260. doi: 10.1007/s10240-020-00114-0
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