Karl ChristBen-Gurion University of the Negev and Leibniz University HannoverXiang HeEinstein Institute of Mathematics and Yau Mathematical Sciences CenterIlya TyomkinBen-Gurion University of the Negev
Journal für die reine und angewandte Mathematik, 2022.4
Yuan-Pin LeeDepartment of Mathematics, University of Utah, Salt Lake City, Utah, 84112Hui-Wen LinTaida Institute of Mathematical Sciences (TIMS), National Taiwan University, Taipei 106Chin-Lung WangTaida Institute of Mathematical Sciences (TIMS), National Taiwan University, Taipei 106
For projective conifold transitions between Calabi-Yau threefolds X and Y, with X close to Y in the moduli, we show that the combined information provided by the A model (Gromov--Witten theory in all genera) and B model (variation of Hodge structures) on X, linked along the vanishing cycles, determines the corresponding combined information on Y. Similar result holds in the reverse direction when linked with the exceptional curves.
A reconstruction theorem for genus 0 gravitational quantum cohomology and quantum K-theory is proved. A new linear equivalence in the Picard group of the moduli space of genus 0 stable maps relating the pull-backs of line bundles from the target via different markings is used for the reconstruction result. Examples of calculations in quantum cohomology and quantum K-theory are given.