Geometry & Topology Volume 21, issue 6 (2017)

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Virtual fundamental classes for moduli spaces of sheaves on Calabi–Yau four-folds

Dennis Borisov and Dominic Joyce

Geometry & Topology 21 (2017) 3231–3311

DOI: 10.2140/gt.2017.21.3231

Bibliography

1	K Behrend, B Fantechi, The intrinsic normal cone, Invent. Math. 128 (1997) 45 MR1437495
2	O Ben-Bassat, C Brav, V Bussi, D Joyce, A “Darboux theorem” for shifted symplectic structures on derived Artin stacks, with applications, Geom. Topol. 19 (2015) 1287 MR3352237
3	D Borisov, Derived manifolds and Kuranishi models, preprint (2012) arXiv:1212.1153
4	D Borisov, J Noel, Simplicial approach to derived differential manifolds, preprint (2011) arXiv:1112.0033
5	C Brav, V Bussi, D Dupont, D Joyce, B Szendrői, Symmetries and stabilization for sheaves of vanishing cycles, J. Singul. 11 (2015) 85 MR3353002
6	C Brav, V Bussi, D Joyce, A “Darboux theorem” for derived schemes with shifted symplectic structure, (2013) arXiv:1305.6302
7	V Bussi, D Joyce, S Meinhardt, On motivic vanishing cycles of critical loci, preprint (2013) arXiv:1305.6428
8	Y Cao, Donaldson–Thomas theory for Calabi–Yau four-folds, preprint (2013) arXiv:1309.4230
9	Y Cao, N C Leung, Donaldson–Thomas theory for Calabi–Yau 4–folds, preprint (2014) arXiv:1407.7659
10	Y Cao, N C Leung, Orientability for gauge theories on Calabi–Yau manifolds, Adv. Math. 314 (2017) 48 MR3658712
11	P E Conner, Differentiable periodic maps, 738, Springer (1979) MR548463
12	S K Donaldson, P B Kronheimer, The geometry of four-manifolds, Oxford Univ. Press (1990) MR1079726
13	S K Donaldson, R P Thomas, Gauge theory in higher dimensions, from: "The geometric universe" (editors S A Huggett, L J Mason, K P Tod, S T Tsou, N M J Woodhouse), Oxford Univ. Press (1998) 31 MR1634503
14	K Fukaya, Y G Oh, H Ohta, K Ono, Lagrangian intersection Floer theory : anomaly and obstruction, I–II, 46, Amer. Math. Soc. (2009) MR2553465
15	K Fukaya, K Ono, Arnold conjecture and Gromov–Witten invariant, Topology 38 (1999) 933 MR1688434
16	R Hartshorne, Algebraic geometry, 52, Springer (1977) MR0463157
17	D Joyce, Algebraic geometry over C^∞–rings, preprint (2009) arXiv:1001.0023
18	D Joyce, D-manifolds and d-orbifolds: a theory of derived differential geometry, book project (2012)
19	D Joyce, D-manifolds, d-orbifolds and derived differential geometry: a detailed summary, preprint (2012) arXiv:1208.4948
20	D Joyce, An introduction to d-manifolds and derived differential geometry, from: "Moduli spaces" (editors L Brambila-Paz, O García-Prada, P Newstead, R P Thomas), London Math. Soc. Lecture Note Ser. 411, Cambridge Univ. Press (2014) 230 MR3221297
21	D Joyce, A new definition of Kuranishi space, preprint (2014) arXiv:1409.6908
22	D Joyce, A classical model for derived critical loci, J. Differential Geom. 101 (2015) 289 MR3399099
23	D Joyce, Kuranishi spaces as a 2–category, preprint (2015) arXiv:1510.07444
24	D Joyce, Kuranishi spaces and symplectic geometry, multiple-volume book project (2017)
25	D Joyce, Y Song, A theory of generalized Donaldson–Thomas invariants, 1020, Amer. Math. Soc. (2012) MR2951762
26	M Kontsevich, Y Soibelman, Stability structures, motivic Donaldson–Thomas invariants and cluster transformations, (2008) arXiv:0811.2435
27	J Lurie, Derived algebraic geometry, V: Structured spaces, preprint (2009) arXiv:0905.0459
28	D McDuff, Notes on Kuranishi atlases, preprint (2014) arXiv:1411.4306
29	D McDuff, K Wehrheim, Kuranishi atlases with trivial isotropy : the 2013 state of affairs, preprint (2012) arXiv:1208.1340
30	J Milnor, On the Steenrod homology theory, from: "Collected papers of John Milnor, IV : Homotopy, homology and manifolds" (editor J McCleary), Amer. Math. Soc. (2009) 83 MR2590677
31	T Pantev, B Toën, M Vaquié, G Vezzosi, Shifted symplectic structures, Publ. Math. Inst. Hautes Études Sci. 117 (2013) 271 MR3090262
32	D I Spivak, Derived smooth manifolds, Duke Math. J. 153 (2010) 55 MR2641940
33	R P Thomas, A holomorphic Casson invariant for Calabi–Yau 3–folds, and bundles on K3 fibrations, J. Differential Geom. 54 (2000) 367 MR1818182
34	B Toën, Higher and derived stacks: a global overview, from: "Algebraic geometry, 1" (editors D Abramovich, A Bertram, L Katzarkov, R Pandharipande, M Thaddeus), Proc. Sympos. Pure Math. 80, Amer. Math. Soc. (2009) 435 MR2483943
35	B Toën, Derived algebraic geometry, EMS Surv. Math. Sci. 1 (2014) 153 MR3285853
36	B Toën, G Vezzosi, Homotopical algebraic geometry, II : Geometric stacks and applications, Amer. Math. Soc. (2008) MR2394633