Towards $A + B$ theory in conifold transitions for Calabi-Yau threefolds

Yuan-Pin Lee; Hui-Wen Lin; Chin-Lung Wang

Towards $A + B$ theory in conifold transitions for Calabi-Yau threefolds

Algebraic Geometry 2017-09-21 v3

Authors: Yuan-Pin Lee , Hui-Wen Lin , Chin-Lung Wang

Abstract

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.

Keywords

conifold transitions Calabi-Yau threefolds A-model B-model Gromov-Witten theory variation of Hodge structures vanishing cycles

Cite

@article{arxiv.1502.03277,
  title  = {Towards $A + B$ theory in conifold transitions for Calabi-Yau threefolds},
  author = {Yuan-Pin Lee and Hui-Wen Lin and Chin-Lung Wang},
  journal= {arXiv preprint arXiv:1502.03277},
  year   = {2017}
}

Comments

47 pages, references updated. To appear in J. Diff. Geometry

Towards $A + B$ theory in conifold transitions for Calabi-Yau threefolds

Abstract

Keywords

Cite

Comments

Related papers