On Donaldson-Thomas invariants of threefold stacks and gerbes
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- by Amin Gholampour and Hsian-Hua Tseng PDF
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Abstract:
We present a construction of Donaldson-Thomas invariants for three-dimensional projective Calabi-Yau Deligne-Mumford stacks. We also study the structure of these invariants for étale gerbes over such stacks.References
- Dan Abramovich, Tom Graber, and Angelo Vistoli, Algebraic orbifold quantum products, Orbifolds in mathematics and physics (Madison, WI, 2001) Contemp. Math., vol. 310, Amer. Math. Soc., Providence, RI, 2002, pp. 1–24. MR 1950940, DOI 10.1090/conm/310/05397
- Dan Abramovich, Tom Graber, and Angelo Vistoli, Gromov-Witten theory of Deligne-Mumford stacks, Amer. J. Math. 130 (2008), no. 5, 1337–1398. MR 2450211, DOI 10.1353/ajm.0.0017
- Kai Behrend, Donaldson-Thomas type invariants via microlocal geometry, Ann. of Math. (2) 170 (2009), no. 3, 1307–1338. MR 2600874, DOI 10.4007/annals.2009.170.1307
- K. Behrend and B. Fantechi, The intrinsic normal cone, Invent. Math. 128 (1997), no. 1, 45–88. MR 1437495, DOI 10.1007/s002220050136
- Andrei Horia Caldararu, Derived categories of twisted sheaves on Calabi-Yau manifolds, ProQuest LLC, Ann Arbor, MI, 2000. Thesis (Ph.D.)–Cornell University. MR 2700538
- Weimin Chen and Yongbin Ruan, Orbifold Gromov-Witten theory, Orbifolds in mathematics and physics (Madison, WI, 2001) Contemp. Math., vol. 310, Amer. Math. Soc., Providence, RI, 2002, pp. 25–85. MR 1950941, DOI 10.1090/conm/310/05398
- Dan Edidin, Brendan Hassett, Andrew Kresch, and Angelo Vistoli, Brauer groups and quotient stacks, Amer. J. Math. 123 (2001), no. 4, 761–777. MR 1844577
- Simeon Hellerman, André Henriques, Tony Pantev, Eric Sharpe, and Matt Ando, Cluster decomposition, $T$-duality, and gerby CFTs, Adv. Theor. Math. Phys. 11 (2007), no. 5, 751–818. MR 2365496
- Luc Illusie, Complexe cotangent et déformations. I, Lecture Notes in Mathematics, Vol. 239, Springer-Verlag, Berlin-New York, 1971 (French). MR 0491680
- D. Joyce and Y. Song. A theory of generalized Donaldson-Thomas invariants. To appear in Mem. Amer. Math. Soc., arXiv:0810.5645v4.
- Andrew Kresch, On the geometry of Deligne-Mumford stacks, Algebraic geometry—Seattle 2005. Part 1, Proc. Sympos. Pure Math., vol. 80, Amer. Math. Soc., Providence, RI, 2009, pp. 259–271. MR 2483938, DOI 10.1090/pspum/080.1/2483938
- Max Lieblich, Moduli of twisted sheaves, Duke Math. J. 138 (2007), no. 1, 23–118. MR 2309155, DOI 10.1215/S0012-7094-07-13812-2
- Max Lieblich, Twisted sheaves and the period-index problem, Compos. Math. 144 (2008), no. 1, 1–31. MR 2388554, DOI 10.1112/S0010437X07003144
- D. Maulik, N. Nekrasov, A. Okounkov, and R. Pandharipande, Gromov-Witten theory and Donaldson-Thomas theory. I, Compos. Math. 142 (2006), no. 5, 1263–1285. MR 2264664, DOI 10.1112/S0010437X06002302
- D. Maulik, N. Nekrasov, A. Okounkov, and R. Pandharipande, Gromov-Witten theory and Donaldson-Thomas theory. II, Compos. Math. 142 (2006), no. 5, 1286–1304. MR 2264665, DOI 10.1112/S0010437X06002314
- F. Nironi. Grothendieck Duality for Projective Deligne-Mumford Stacks. arXiv:0811.1955.
- F. Nironi. Moduli Spaces of Semistable Sheaves on Projective Deligne-Mumford Stacks. arXiv:0811.1949v1.
- Martin Olsson and Jason Starr, Quot functors for Deligne-Mumford stacks, Comm. Algebra 31 (2003), no. 8, 4069–4096. Special issue in honor of Steven L. Kleiman. MR 2007396, DOI 10.1081/AGB-120022454
- X. Tang and H.-H. Tseng. Duality theorems of étale gerbes on orbifolds. arXiv:1004.1376.
- 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. MR 1818182
- Daniel Huybrechts and Richard P. Thomas, Deformation-obstruction theory for complexes via Atiyah and Kodaira-Spencer classes, Math. Ann. 346 (2010), no. 3, 545–569. MR 2578562, DOI 10.1007/s00208-009-0397-6
Additional Information
- Amin Gholampour
- Affiliation: Department of Mathematics, Imperial College London, South Kensington Campus, London SW7 2AZ, United Kingdom
- Address at time of publication: Department of Mathematics, University of Maryland, 1301 Mathematics Building, College Park, Maryland 20742-4015
- Email: a.gholampour@imperial.ac.uk, amingh@umd.edu
- Hsian-Hua Tseng
- Affiliation: Department of Mathematics, Ohio State University, 100 Math Tower, 231 West 18th Avenue, Columbus, Ohio 43210
- Email: hhtseng@math.ohio-state.edu
- Received by editor(s): February 9, 2011
- Received by editor(s) in revised form: May 12, 2011, June 1, 2011, and June 22, 2011
- Published electronically: May 25, 2012
- Communicated by: Lev Borisov
- © Copyright 2012
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Proc. Amer. Math. Soc. 141 (2013), 191-203
- MSC (2010): Primary 14N35
- DOI: https://doi.org/10.1090/S0002-9939-2012-11346-2
- MathSciNet review: 2988722