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STABLE QUASIMAPS
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 Title & Authors
STABLE QUASIMAPS
Kim, Bum-Sig;
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 Abstract
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.
 Keywords
Gromov-Witten theory;GIT quotients;curves;twisted quiver bundles;symmetric obstruction theory;
 Language
English
 Cited by
 References
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. crossref(new window)

3.
K. Behrend and B. Fantechi, The intrinsic normal cone, Invent. Math. 128 (1997), no. 1, 45-88. crossref(new window)

4.
A. Bertram, Quantum Schubert calculus, Adv. Math. 128 (1997), no. 2, 289-305. crossref(new window)

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. crossref(new window)

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. crossref(new window)

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. crossref(new window)

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. crossref(new window)

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. crossref(new window)

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.

31.
R. Pandharipande and R. P. Thomas, Curve counting via stable pairs in the derived category, Invent. Math. 178 (2009), no. 2, 407-447. crossref(new window)

32.
B. Szendroi, Non-commutative Donaldson-Thomas invariants and the conifold, Geom. Topol. 12 (2008), no. 2, 1171-1202. crossref(new window)

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.

34.
Y. Toda, Moduli spaces of stable quotients and the wall-crossing phenomena, arXiv:1005.3743.