Geometry & Topology Volume 15, issue 3 (2011)

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Non-commutative Donaldson–Thomas theory and vertex operators

Kentaro Nagao

Geometry & Topology 15 (2011) 1509–1543

DOI: 10.2140/gt.2011.15.1509

Bibliography

1	M Aganagic, A Klemm, M Mariño, C Vafa, The topological vertex, Comm. Math. Phys. 254 (2005) 425 MR2117633
2	K Behrend, Donaldson–Thomas type invariants via microlocal geometry, Ann. of Math. $(2)$ 170 (2009) 1307 MR2600874
3	K Behrend, B Fantechi, The intrinsic normal cone, Invent. Math. 128 (1997) 45 MR1437495
4	K Behrend, B Fantechi, Symmetric obstruction theories and Hilbert schemes of points on threefolds, Algebra Number Theory 2 (2008) 313 MR2407118
5	M van den Bergh, Non-commutative crepant resolutions arXiv:math/0211064
6	M van den Bergh, Three-dimensional flops and noncommutative rings, Duke Math. J. 122 (2004) 423 MR2057015
7	R Bocklandt, Calabi–Yau algebras and weighted quiver polyhedra arXiv:0905.0232
8	T Bridgeland, t-structures on some local Calabi–Yau varieties, J. Algebra 289 (2005) 453 MR2142382
9	T Bridgeland, Stability conditions on triangulated categories, Ann. of Math. $(2)$ 166 (2007) 317 MR2373143
10	N Broomhead, Dimer models and Calabi–Yau algebras arXiv:0901.4662
11	J Bryan, C Cadman, B Young, The orbifold topological vertex arXiv:1008.4205
12	J Bryan, B Young, Generating functions for colored 3D Young diagrams and the Donaldson–Thomas invariants of orbifolds, Duke Math. J. 152 (2010) 115 MR2643058
13	W Y Chuang, G Pan, Bogomolny–Prasad–Sommerfeld state counting in local obstructed curves from quiver theory and Seiberg duality, J. Math. Phys. 51 (2010) 052305, 22 MR2666961
14	B Davison, Consistency conditions for brane tilings arXiv:0812.4185
15	A Hanany, D Vegh, Quivers, tilings, branes and rhombi, J. High Energy Phys. (2007) 029, 35 MR2357949
16	D Happel, I Reiten, S O Smalø, Tilting in abelian categories and quasitilted algebras, Mem. Amer. Math. Soc. 120 (1996) MR1327209
17	A Ishii, K Ueda, Dimer models and the special McKay correspondence arXiv:0905.0059
18	A Ishii, K Ueda, On moduli spaces of quiver representations associated with dimer models arXiv:0710.1898
19	D Joyce, Configurations in abelian categories IV: Invariants and changing stability conditions, Adv. Math. 217 (2008) 125 MR2357325
20	D Joyce, Y Song, A theory of generalzed Donaldson–Thomas invariants arXiv:0810.5645
21	D Maulik, N Nekrasov, A Okounkov, R Pandharipande, Gromov–Witten theory and Donaldson–Thomas theory I, Compos. Math. 142 (2006) 1263 MR2264664
22	S Mozgovoy, Crepant resolutions and brane tilings I: Toric realization arXiv:0908.3475
23	S Mozgovoy, M Reineke, On the noncommutative Donaldson–Thomas invariants arising from brane tilings, Adv. Math. 223 (2010) 1521 MR2592501
24	K Nagao, Derived categories of small 3–dimensional toric Calabi–Yau varieties and curve counting invariants arXiv:0809.2994
25	K Nagao, Quiver varieties and Frenkel–Kac construction, J. Algebra 321 (2009) 3764 MR2517812
26	K Nagao, Refined open non-commutative Donaldson–Thomas theory for small toric Calabi–Yau 3–folds, Pacific J. Math. (to appear) arXiv:0907.3784
27	K Nagao, H Nakajima, Counting invariants of perverse coherent systems on 3–folds and their wall-crossings, Int. Math. Res. Not. 46 (2010)
28	K Nagao, M Yamazaki, The non-commutative topological vertex and wall crossing phenomena (to appear) arXiv:0910.5479
29	A Okounkov, N Reshetikhin, C Vafa, Quantum Calabi–Yau and classical crystals, from: "The unity of mathematics", Progr. Math. 244, Birkhäuser (2006) 597 MR2181817
30	H Ooguri, M Yamazaki, Crystal melting and toric Calabi–Yau manifolds, Comm. Math. Phys. 292 (2009) 179 MR2540074
31	R Pandharipande, R P Thomas, Curve counting via stable pairs in the derived category, Invent. Math. 178 (2009) 407 MR2545686
32	P Sułkowski, Wall-crossing, free fermions and crystal melting, Comm. Math. Phys. 301 (2011) 517 MR2764996
33	B Szendrői, Non-commutative Donaldson–Thomas invariants and the conifold, Geom. Topol. 12 (2008) 1171 MR2403807
34	B Young, Computing Donaldson–Thomas partition functions for brane tilings using vertex operators (to appear)