Quasimap SYZ for toric Calabi-Yau manifolds

Kwokwai Chan

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Quasimap SYZ for toric Calabi-Yau manifolds

Kwokwai Chan

Symplectic Geometry · Submitted 6 Apr 2017

abstract compiled · 2026-09-23 · no language-model review

The authors' main claim We show that the resulting SYZ mirror coincides with the one written down via physical means (as expected).

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In this note, we study the SYZ mirror construction for a toric Calabi-Yau manifold using instanton corrections coming from Woodward's quasimap Floer theory instead of Fukaya-Oh-Ohta-Ono's Lagrangian Floer theory. We show that the resulting SYZ mirror coincides with the one written down via physical means (as expected).

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#	sentence	role	the authors' own work	states the main conclusion	strength
s0	In this note, we study the SYZ mirror construction for a toric Calabi-Yau manifold using instanton corrections coming from Woodward's quasimap Floer theory instead of Fukaya-Oh-Ohta-Ono's Lagrangian Floer theory.	contribution 0.91	0.76	0.12	asserted 0.86
s1	We show that the resulting SYZ mirror coincides with the one written down via physical means (as expected).	result 0.99	0.90	0.81	asserted 1.00

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Original abstract

In this note, we study the SYZ mirror construction for a toric Calabi-Yau manifold using instanton corrections coming from Woodward's quasimap Floer theory instead of Fukaya-Oh-Ohta-Ono's Lagrangian Floer theory. We show that the resulting SYZ mirror coincides with the one written down via physical means (as expected).

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Each citing sentence is taken from the citing paper's LaTeX source and typed by Pith's classifier. A label appears at probability 0.8 or more (0.95 for support), a contest at 0.7 or more; the quoted words are the citing authors'. How each label was checked · JSON

What it cites · 4 sentences without a confident label

Compares with 2 papers

The function $W^QF$ coincides with the Givental-Hori-Vafa superpotential [ref] for the toric manifold $X$.

Mirror Symmetry · Woodward's quasimap Floer theory · 0.97
Notice that the quasimap SYZ mirror family [ref] is entirely written in terms of symplectic-geometric information such as complexified Kähler parameters and quasidisk invariants of $X$, and it coincides with the mirror [ref] predicted by physical arguments [ref] .

D-Branes And Mirror Symmetry · Wall-crossing for quasidisk invariants and the SYZ mirror · 0.97

Cites as background 4 papers

In [ref] (see also [ref] ), Woodward developed a quasimap Floer theory as the zero-area limit of Frauenfelder's gauged Lagrangian Floer theory [ref] .

Gauged Floer theory of toric moment fibers · Woodward's quasimap Floer theory · 0.87
The mirror of a toric Calabi-Yau manifold $X$ is predicted to be a family of affine hypersurfaces in $^2 ×(^×)^n-1$ [ref] explicitly written as [equation] where the coefficients $Č_i ∈$ are constants (without loss of generality, we will set $Č_m = 1$) subject to the constraints [equation] here $t = (t_1, …, t_r)$ are coordinates on the mirror complex moduli $ℳ̌_B := 𝕂^∨⊗_ ^×≅(^×)^r$. $X̌_t$ is Calabi-Yau since [equation] is a nowhere vanishing holomorphic volume form on $X̌_t$.

Mirror Symmetry · Toric Calabi-Yau manifolds and their physical mirrors · 0.89
The mirror of a toric Calabi-Yau manifold $X$ is predicted to be a family of affine hypersurfaces in $^2 ×(^×)^n-1$ [ref] explicitly written as [equation] where the coefficients $Č_i ∈$ are constants (without loss of generality, we will set $Č_m = 1$) subject to the constraints [equation] here $t = (t_1, …, t_r)$ are coordinates on the mirror complex moduli $ℳ̌_B := 𝕂^∨⊗_ ^×≅(^×)^r$. $X̌_t$ is Calabi-Yau since [equation] is a nowhere vanishing holomorphic volume form on $X̌_t$.

D-Branes And Mirror Symmetry · Toric Calabi-Yau manifolds and their physical mirrors · 0.89

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