Relative Gromov-Witten invariants and the enumerative meaning of mirror maps for toric Calabi-Yau orbifolds
Fenglong You
TL;DR
This paper establishes a connection between mirror maps and relative Gromov-Witten invariants for toric Calabi-Yau orbifolds, enabling the construction of instanton corrected mirrors through enumerative geometry.
Contribution
It provides an enumerative interpretation of mirror maps via relative Gromov-Witten invariants and links them to open invariants for toric Calabi-Yau orbifolds.
Findings
Equality between relative and open Gromov-Witten invariants
Mirror maps have an enumerative meaning in terms of relative invariants
Construction of instanton corrected mirrors using relative Gromov-Witten invariants
Abstract
We provide an enumerative meaning of the mirror maps for toric Calabi-Yau orbifolds in terms of relative Gromov-Witten invariants of the toric compactifications. As a consequence, we obtain an equality between relative Gromov-Witten invariants and open Gromov-Witten invariants. Therefore, the instanton corrected mirrors for toric Calabi-Yau orbifolds can be constructed using relative Gromov-Witten invariants.
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Taxonomy
TopicsAlgebraic Geometry and Number Theory · Geometric and Algebraic Topology · Advanced Algebra and Geometry