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arxiv: 1806.08442 · v1 · submitted 2018-06-21 · 🧮 math.AG · math-ph· math.MP

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Wall-crossing in genus-zero hybrid theory

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classification 🧮 math.AG math-phmath.MP
keywords hybridtheorygenus-zerowall-crossingworkauthorcalabi-yaucomplete
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The hybrid model is the Landau-Ginszburg-type theory that is expected, via the Landau-Ginzburg/Calabi-Yau correspondence, to match the Gromov-Witten theory of a complete intersection in weighted projective space. We prove a wall-crossing formula exhibiting the dependence of the genus-zero hybrid model on its stability parameter, generalizing the work of the second author and Ruan for quantum singularity theory and paralleling the work of Ciocan-Fontanine--Kim for quasimaps. This completes the proof of the genus-zero Landau-Ginzburg/Calabi-Yau correspondence for complete intersections of hypersurfaces of the same degree, as well as the proof of the all-genus hybrid wall-crossing theorem, which is work of the first author, Janda, and Ruan.

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