Quantum McKay correspondence for disc invariants of toric Calabi-Yau 3-orbifolds

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• 作者：Hua-Zhong Ke (1)
  Jian Zhou (1)
  
• 关键词：Quantum McKay correspondence ; disc invariants ; open mirror symmetry ; 14N35
• 刊名：Acta Mathematica Sinica
• 出版年：2015
• 出版时间：January 2015
• 年：2015
• 卷：31
• 期：1
• 页码：29-34
• 全文大小：181 KB
• 参考文献：1. Aganagic, M., Klemm, A., Mari?o, M., et al.: The topological vertex. / Comm. Math. Phys., 254(2), 425-78 (2005) CrossRef
  2. Aganagic, M., Klemm, A., Vafa, C.: Disk instantons, mirror symmetry and the duality web. / Z. Naturforsch. A, 57(1-), 1-8 (2002)
  3. Aganagic, M., Vafa, C.: Mirror symmetry, D-branes and counting holomorphic discs, preprint, hepth/0012041
  4. Brini, A., Cavalieri, R.: Open orbifold Gromov-Witten invariants of [?sup class="a-plus-plus">3/?sub class="a-plus-plus">n]: localization and mirror symmetry. / Selecta Math. ( / N.S.), 17(4), 879-33 (2011) CrossRef
  5. Brini, A., Cavalieri, R., Ross, D.: Crepant resolutions and open strings. math.AG/1309.4438v2
  6. Bryan, J., Graber, T.: The crepant resolution conjecture. Algebraic geometry-Seattle 2005. Part 1, 2-2, Proc. Sympos. Pure Math., 80,Part 1, Amer. Math. Soc., Providence, RI, 2009
  7. Bouchard, V., Klemm, A., Mari?o, M., et al.: Remodeling the B-model. / Comm. Math. Phys., 287(1), 117-78 (2009) CrossRef
  8. Bouchard, V., Klemm, A., Mari?o, M., et al.: Topological open strings on orbifolds. / Comm. Math. Phys., 296(3), 589-23 (2010) CrossRef
  9. Chan, K., Cho, C.-H., Lau, S.-C., et al.: Gross fibration, SYZ mirror symmetry, and open Gromov-Witten invariants for toric Calabi-Yau orbifolds. math.SG/1306.0437v3
  10. Chan, K., Cho, C.-H., Lau, S.-C., et al.: Lagrangian Floer superpotentials and crepant resolutions for toric orbifolds. / Comm. Math. Phys., 328(1), 83-30 (2014) CrossRef
  11. Chiang, T.-M., Klemm, A., Yau, S.-T., et al.: Local mirror symmetry: calculations and interpretations. / Adv. Theor. Math. Phys., 3(3), 495-65 (1999)
  12. Cox, D., Little, J., Schenck, H.: Toric varieties. Graduate Studies in Mathematics, 124, American Mathematical Society, Providence, RI, 2011
  13. Coates, T., Corti, A., Iritani, H., et al.: Computing genus-zero twisted Gromov-Witten invariants. / Duke Math. J., 147(3), 377-38 (2009) CrossRef
  14. Cavalieri, R., Ross, D.: Open Gromov-Witten theory and the crepant resolution conjecture. / Michigan Math. J., 61(4), 807-37 (2012) CrossRef
  15. Fang, B., Liu, C.-C.: Open Gromov-Witten invariants of toric Calabi-Yau 3-folds. / Comm. Math. Phys., 323(1), 285-28 (2013) CrossRef
  16. Fang, B., Liu, C.-C., Tseng, H.-H.: Open-closed Gromov-Witten invariants of 3-dimensional Calabi-Yau smooth toric DM stacks. math.AG/1212.6073
  17. Graber, T., Pandharipande, R.: Localization of virtual classes. / Invent. Math., 135(2), 487-18 (1999) CrossRef
  18. Hu, X.: The quantum McKay correspondence for singularities of type D. / Adv. Math., 247, 266308 (2013) CrossRef
  19. Ke, H.-Z., Zhou, J.: Quantum McKay correspondence for disc invariants of orbifold vertex. arXiv:1410.4374
  20. Ke, H.-Z., Zhou, J.: Gauged linear sigma model for disc invariants. / Lett. Math. Phys., accepted
  21. Li, J., Liu, C.-C., Liu, K., et al.: A mathematical theory of the topological vertex. / Geom. Topol., 13(1), 527-21 (2009) CrossRef
  22. Lerche, W., Mayr, P.: On / N = 1 mirror symmet
• 作者单位：Hua-Zhong Ke (1)
  Jian Zhou (1)
  
  1. Department of Mathematical Sciences, Tsinghua University, Beijing, 100084, P. R. China
  
• ISSN：1439-7617

文摘

We announce a result on quantum McKay correspondence for disc invariants of outer legs in toric Calabi-Yau 3-orbifolds, and illustrate our method in a special example [?sup class="a-plus-plus">3/?sub class="a-plus-plus">5(1, 1, 3)].