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STABLE QUASIMAPS

  • Kim, Bum-Sig (School of Mathematics Korea Institute for Advanced Study)
  • 투고 : 2011.01.13
  • 발행 : 2012.07.31

초록

The moduli spaces of stable quasimaps unify various moduli appearing in the study of Gromov-Witten theory. This note is a survey article on the moduli of stable quasimaps, based on papers [9, 11, 18] as well as the author's talk at Kinosaki Algebraic Geometry Symposium 2010.

키워드

참고문헌

  1. M. Audin, The Topology of Torus Actions on Symplectic Manifolds, Progress in Mathematics, Vol 93, Birkhauser Verlag, Basel, 1991.
  2. K. Behrend, Donaldson-Thomas type invariants via microlocal geometry, Ann. of Math. (2) 170 (2009), no. 3, 1307-1338. https://doi.org/10.4007/annals.2009.170.1307
  3. K. Behrend and B. Fantechi, The intrinsic normal cone, Invent. Math. 128 (1997), no. 1, 45-88. https://doi.org/10.1007/s002220050136
  4. A. Bertram, Quantum Schubert calculus, Adv. Math. 128 (1997), no. 2, 289-305. https://doi.org/10.1006/aima.1997.1627
  5. A. Bertram, I. Ciocan-Fontanine, and B. Kim Gromov-Witten invariants for abelian and nonabelian quotients, J. Algebraic Geom. 17 (2008), no. 2, 275-294. https://doi.org/10.1090/S1056-3911-07-00456-0
  6. D. Cheong, in preparation.
  7. W.-E. Chuang, D. E. Diaconescu, and G. Pan, Chamber structure and wallcrossing in the ADHM theory of curves II, arXiv:0908.1119.
  8. W.-E. Chuang, D. E. Diaconescu, and G. Pan, Rank two ADHM invariants and wallcrossing, arXiv:1002.0579.
  9. I. Ciocan-Fontanine and B. Kim, Moduli stacks of stable toric quasimaps, Adv. Math. 225 (2010), no. 6, 3022-3051. https://doi.org/10.1016/j.aim.2010.05.023
  10. I. Ciocan-Fontanine and B. Kim, in preparation.
  11. I. Ciocan-Fontanine, B. Kim, and D. Maulik, Stable quasimaps to GIT quotients, in preparation.
  12. D. Cox, The homogeneous coordinate ring of a toric variety, J. Algebraic Geom. 4 (1995), no. 1, 17-50.
  13. D.-E. Diaconescu, Chamber structure and wallcrossing in the ADHM theory of curves I, arXive:0904.4451.
  14. I. Dolgachev, Lectures on Invariant Theory, London Mathematical Society Lecture Note Series, 296. Cambridge University Press, Cambridge, 2003.
  15. V. Ginzburg, Lectures on Nakajima's quiver varieties, arXiv:0905.0686.
  16. A. Givental, A mirror theorem for toric complete intersections, Topological field theory, primitive forms and related topics (Kyoto, 1996), 141-175, Progr.Math., 160, Birkhauser Boston, Boston, MA, 1998.
  17. D. Joyce and Y. Song, A theory of generalized Donaldson-Thomas invariants, to appear in Memoirs of the AMS, arXiv:0810.5645.
  18. B. Kim, Stable quasimaps to holomorphic symplectic quotients, arXiv:1005.4125.
  19. B. Kim and H. Lee, Wall-crossings for twisted quiver bundles, arXiv:1101.4156.
  20. A. D. King, Moduli of representations of finite-dimensional algebras, Quart. J. Math. Oxford Ser. (2) 45 (1994), no. 180, 515-530. https://doi.org/10.1093/qmath/45.4.515
  21. M. Kontsevich and Y. Soibelman, Stability structures, motivic Donaldson-Thomas invariants and cluster transformations, arXiv:0811.2435.
  22. A. Kresch, Cycle groups for Artin stacks, Invent. Math. 138 (1999), no. 3, 495-536. https://doi.org/10.1007/s002220050351
  23. G. Laumon and L. Moret-Bailly, Champs algebriques, A Series of Modern Surveys in Mathematics, 39. Springer-Verlag, Berlin, 2000.
  24. J. Lepotier, Lectures on Vector Bundles, Translated by A. Maciocia. Cambridge Studies in Advanced Mathematics, 54. Cambridge University Press, Cambridge, 1997.
  25. J. Li and G. Tian, Virtual moduli cycles and Gromov-Witten invariants of algebraic varieties, J. Amer. Math. Soc. 11 (1998), no. 1, 119-174. https://doi.org/10.1090/S0894-0347-98-00250-1
  26. A. Marian, D. Oprea, and R. Pandharipande, The moduli space of stable quotients, arXiv:0904.2992.
  27. A. Mustata and A. Mustata, Intermediate moduli spaces of stable maps, Invent. Math. 167 (2007), no. 1, 47-90.
  28. A. Mustata and A. Mustata, The Chow ring of ${\bar{M}}_{0,m}$(${\mathbb{P}}^n$, d), J. Reine Angew. Math. 615 (2008), 93-119.
  29. C. Okonek, M. Schneider, and H. Spindler, Vector Bundles on Complex Projective Spaces, Progress in Mathematics, Vol 3, Birkhauser, Boston, Mass., 1980.
  30. C. Okonek and A. Teleman, Comparing virtual fundamental classes: gauge theoretical Gromov-Witten invariants for toric varieties, Asian J. Math. 7 (2003), no. 2, 167-198. https://doi.org/10.4310/AJM.2003.v7.n2.a2
  31. R. Pandharipande and R. P. Thomas, Curve counting via stable pairs in the derived category, Invent. Math. 178 (2009), no. 2, 407-447. https://doi.org/10.1007/s00222-009-0203-9
  32. B. Szendroi, Non-commutative Donaldson-Thomas invariants and the conifold, Geom. Topol. 12 (2008), no. 2, 1171-1202. https://doi.org/10.2140/gt.2008.12.1171
  33. R. P. Thomas, A holomorphic Casson invariant for Calabi-Yau 3-folds, and bundles on K3 fibrations, J. Differential Geom. 54 (2000), no. 2, 367-438. https://doi.org/10.4310/jdg/1214341649
  34. Y. Toda, Moduli spaces of stable quotients and the wall-crossing phenomena, arXiv:1005.3743.

피인용 문헌

  1. A mathematical theory of the gauged linear sigma model vol.22, pp.1, 2017, https://doi.org/10.2140/gt.2018.22.235