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Monopole contributions to refined Vafa–Witten invariants

Ties Laarakker

Geometry & Topology 24 (2020) 2781–2828
DOI: 10.2140/gt.2020.24.2781
Bibliography
1 E Carlsson, A Okounkov, Exts and vertex operators, Duke Math. J. 161 (2012) 1797 MR2942794
2 G Ellingsrud, L Göttsche, M Lehn, On the cobordism class of the Hilbert scheme of a surface, J. Algebraic Geom. 10 (2001) 81 MR1795551
3 B Fantechi, L Göttsche, Riemann–Roch theorems and elliptic genus for virtually smooth schemes, Geom. Topol. 14 (2010) 83 MR2578301
4 A Gholampour, A Sheshmani, S T Yau, Localized Donaldson–Thomas theory of surfaces, Amer. J. Math. 142 (2020) 405 MR4084159
5 A Gholampour, A Sheshmani, S T Yau, Nested Hilbert schemes on surfaces : virtual fundamental class, Adv. Math. 365 (2020) 107046 MR4064771
6 A Gholampour, R P Thomas, Degeneracy loci, virtual cycles and nested Hilbert schemes, I, Tunis. J. Math. 2 (2020) 633 MR4041285
7 A Gholampour, R P Thomas, Degeneracy loci, virtual cycles and nested Hilbert schemes, II, Compos. Math. 156 (2020) 1623
8 L Göttsche, The Betti numbers of the Hilbert scheme of points on a smooth projective surface, Math. Ann. 286 (1990) 193 MR1032930
9 L Göttsche, A conjectural generating function for numbers of curves on surfaces, Comm. Math. Phys. 196 (1998) 523 MR1645204
10 L Göttsche, M Kool, Refined SU(3) Vafa–Witten invariants and modularity, Pure Appl. Math. Q. 14 (2018) 467 MR4047406
11 L Göttsche, M Kool, Virtual refinements of the Vafa–Witten formula, Comm. Math. Phys. 376 (2020) 1 MR4093873
12 L Göttsche, H Nakajima, K Yoshioka, Instanton counting and Donaldson invariants, J. Differential Geom. 80 (2008) 343 MR2472477
13 L Göttsche, W Soergel, Perverse sheaves and the cohomology of Hilbert schemes of smooth algebraic surfaces, Math. Ann. 296 (1993) 235 MR1219901
14 T Graber, R Pandharipande, Localization of virtual classes, Invent. Math. 135 (1999) 487 MR1666787
15 T Laarakker, Vertical Vafa–Witten invariants, (2019) arXiv:1906.01264
16 Y P Lee, R Pandharipande, Algebraic cobordism of bundles on varieties, J. Eur. Math. Soc. 14 (2012) 1081 MR2928845
17 D Maulik, N Nekrasov, A Okounkov, R Pandharipande, Gromov–Witten theory and Donaldson–Thomas theory, I, Compos. Math. 142 (2006) 1263 MR2264664
18 T Mochizuki, Donaldson type invariants for algebraic surfaces, 1972, Springer (2009) MR2508583
19 T S Developers, SageMath : the Sage mathematics software system, version 6.10 (2015)
20 Y Tanaka, R P Thomas, Vafa–Witten invariants for projective surfaces, I : Stable case, J. Algebraic Geom. 29 (2020) 603
21 R P Thomas, Equivariant K–theory and refined Vafa–Witten invariants, Comm. Math. Phys. (2020)
22 C Vafa, E Witten, A strong coupling test of S–duality, Nuclear Phys. B 431 (1994) 3 MR1305096