A Note on Disk Counting in Toric Orbifolds
Symmetry, integrability and geometry: methods and applications, Tome 16 (2020) Cet article a éte moissonné depuis la source Math-Net.Ru

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We compute orbi-disk invariants of compact Gorenstein semi-Fano toric orbifolds by extending the method used for toric Calabi–Yau orbifolds. As a consequence the orbi-disc potential is analytic over complex numbers.
Keywords: orbifold, toric, open Gromov–Witten invariants, mirror symmetry, SYZ.
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     author = {Kwokwai Chan and Cheol-Hyun Cho and Siu-Cheong Lau and Naichung Conan Leung and Hsian-Hua Tseng},
     title = {A {Note} on {Disk} {Counting} in {Toric} {Orbifolds}},
     journal = {Symmetry, integrability and geometry: methods and applications},
     year = {2020},
     volume = {16},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SIGMA_2020_16_a54/}
}
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Kwokwai Chan; Cheol-Hyun Cho; Siu-Cheong Lau; Naichung Conan Leung; Hsian-Hua Tseng. A Note on Disk Counting in Toric Orbifolds. Symmetry, integrability and geometry: methods and applications, Tome 16 (2020). http://geodesic.mathdoc.fr/item/SIGMA_2020_16_a54/

[1] Auroux D., “Mirror symmetry and $T$-duality in the complement of an anticanonical divisor”, J. Gökova Geom. Topol., 1 (2007), 51–91, arXiv: 0706.3207 | MR | Zbl

[2] Borisov L. A., Chen L., Smith G. G., “The orbifold Chow ring of toric Deligne–Mumford stacks”, J. Amer. Math. Soc., 18 (2005), 193–215, arXiv: math.AG/0309229 | DOI | MR | Zbl

[3] Chan K., Cho C.-H., Lau S.-C., Tseng H.-H., “Lagrangian Floer superpotentials and crepant resolutions for toric orbifolds”, Comm. Math. Phys., 328 (2014), 83–130, arXiv: 1208.5282 | DOI | MR | Zbl

[4] Chan K., Cho C.-H., Lau S.-C., Tseng H.-H., “Gross fibrations, SYZ mirror symmetry, and open Gromov–Witten invariants for toric Calabi–Yau orbifolds”, J. Differential Geom., 103 (2016), 207–288, arXiv: 1306.0437 | DOI | MR | Zbl

[5] Chan K., Lau S.-C., Leung N. C., Tseng H.-H., “Open Gromov–Witten invariants, mirror maps, and Seidel representations for toric manifolds”, Duke Math. J., 166 (2017), 1405–1462, arXiv: 1209.6119 | DOI | MR | Zbl

[6] Chen W., Ruan Y., “Orbifold Gromov–Witten theory”, Orbifolds in Mathematics and Physics (Madison, WI, 2001), Contemp. Math., 310, Amer. Math. Soc., Providence, RI, 2002, 25–85, arXiv: math.AG/0103156 | DOI | MR | Zbl

[7] Chen W., Ruan Y., “A new cohomology theory of orbifold”, Comm. Math. Phys., 248 (2004), 1–31, arXiv: math.AG/0004129 | DOI | MR | Zbl

[8] Cho C.-H., Oh Y.-G., “Floer cohomology and disc instantons of Lagrangian torus fibers in Fano toric manifolds”, Asian J. Math., 10 (2006), 773–814, arXiv: math.SG/0308225 | DOI | MR | Zbl

[9] Cho C.-H., Poddar M., “Holomorphic orbi-discs and Lagrangian Floer cohomology of symplectic toric orbifolds”, J. Differential Geom., 98 (2014), 21–116, arXiv: 1206.3994 | DOI | MR | Zbl

[10] Cho C.-H., Shin H.-S., “Chern–Weil Maslov index and its orbifold analogue”, Asian J. Math., 20 (2016), 1–19, arXiv: 1202.0556 | DOI | MR

[11] Coates T., Corti A., Iritani H., Tseng H.-H., “A mirror theorem for toric stacks”, Compos. Math., 151 (2015), 1878–1912, arXiv: 1310.4163 | DOI | MR | Zbl

[12] Cox D. A., Little J. B., Schenck H. K., Toric varieties, Graduate Studies in Mathematics, 124, Amer. Math. Soc., Providence, RI, 2011 | DOI | MR | Zbl

[13] Fukaya K., Oh Y.-G., Ohta H., Ono K., Lagrangian intersection Floer theory: anomaly and obstruction, AMS/IP Studies in Advanced Mathematics, 46, Amer. Math. Soc., Providence, RI, 2009 | MR

[14] Fukaya K., Oh Y.-G., Ohta H., Ono K., “Lagrangian Floer theory on compact toric manifolds. I”, Duke Math. J., 151 (2010), 23–174, arXiv: 0802.1703 | DOI | MR

[15] Fukaya K., Oh Y.-G., Ohta H., Ono K., “Lagrangian Floer theory on compact toric manifolds II: bulk deformations”, Selecta Math. (N.S.), 17 (2011), 609–711, arXiv: 0810.5654 | DOI | MR | Zbl

[16] Fukaya K., Oh Y.-G., Ohta H., Ono K., Technical details on Kuranishi structure and virtual fundamental chain, arXiv: 1209.4410

[17] Fukaya K., Oh Y.-G., Ohta H., Ono K., “Lagrangian Floer theory and mirror symmetry on compact toric manifolds”, Astérisque, 376, 2016, vi+340 pp., arXiv: 1009.1648 | MR | Zbl

[18] González E., Iritani H., “Seidel elements and mirror transformations”, Selecta Math. (N.S.), 18 (2012), 557–590, arXiv: 1103.4171 | DOI | MR | Zbl

[19] Gross M., Siebert B., “From real affine geometry to complex geometry”, Ann. of Math., 174 (2011), 1301–1428, arXiv: math.AG/0703822 | DOI | MR | Zbl

[20] Hausel T., Sturmfels B., “Toric hyper{K}ähler varieties”, Doc. Math., 7 (2002), 495–534, arXiv: math.AG/0203096 | MR | Zbl

[21] Iritani H., “An integral structure in quantum cohomology and mirror symmetry for toric orbifolds”, Adv. Math., 222 (2009), 1016–1079, arXiv: 0903.1463 | DOI | MR | Zbl

[22] Jiang Y., “The orbifold cohomology ring of simplicial toric stack bundles”, Illinois J. Math., 52 (2008), 493–514, arXiv: math.AG/0504563 | DOI | MR | Zbl

[23] McDuff D., Wehrheim K., “Smooth Kuranishi atlases with isotropy”, Geom. Topol., 21 (2017), 2725–2809, arXiv: 1508.01556 | DOI | MR | Zbl

[24] Ruddat H., Siebert B., “Period integrals from wall structures via tropical cycles, canonical coordinates in mirror symmetry and analyticity of toric degenerations”, Publ. Math. Inst. Hautes Études Sci. (to appear) | DOI | MR

[25] Strominger A., Yau S.-T., Zaslow E., “Mirror symmetry is $T$-duality”, Nuclear Phys. B, 479 (1996), 243–259, arXiv: hep-th/9606040 | DOI | MR | Zbl