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Equivariant Gromov-Witten Theory of GKM Orbifolds

Zhengyu Zong

Title:
Equivariant Gromov-Witten Theory of GKM Orbifolds
Author(s):
Zong, Zhengyu
Thesis Advisor(s):
Liu, Chiu-Chu M.
Date:
Type:
Theses
Degree:
Ph.D., Columbia University
Department(s):
Mathematics
Persistent URL:
Abstract:
In this paper, we study the all genus Gromov-Witten theory for any GKM orbifold X. We generalize the Givental formula which is studied in the smooth case in [41] [42] [43] to the orbifold case. Specifically, we recover the higher genus Gromov-Witten invariants of a GKM orbifold X by its genus zero data. When X is toric, the genus zero Gromov-Witten invariants of X can be explicitly computed by the mirror theorem studied in [22] and our main theorem gives a closed formula for the all genus Gromov-Witten invariants of X. When X is a toric Calabi-Yau 3-orbifold, our formula leads to a proof of the remodeling conjecture in [38]. The remodeling conjecture can be viewed as an all genus mirror symmetry for toric Calabi-Yau 3-orbifolds. In this case, we apply our formula to the A-model higher genus potential and prove the remodeling conjecture by matching it to the B-model higher genus potential.
Subject(s):
Mathematics
Item views
490
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Suggested Citation:
Zhengyu Zong, , Equivariant Gromov-Witten Theory of GKM Orbifolds, Columbia University Academic Commons, .

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