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Quot schemes of curves and surfaces: virtual classes, integrals, Euler characteristics

Dragos Oprea and Rahul Pandharipande

Geometry & Topology 25 (2021) 3425–3505
Bibliography
1 N Arbesfeld, D Johnson, W Lim, D Oprea, R Pandharipande, The virtual K–theory of Quot schemes of surfaces, J. Geom. Phys. 164 (2021) MR4220750
2 J C Aval, Multivariate Fuss–Catalan numbers, Discrete Math. 308 (2008) 4660 MR2438172
3 W Barth, C Peters, A Van de Ven, Compact complex surfaces, 4, Springer (1984) MR749574
4 A Bertram, Towards a Schubert calculus for maps from a Riemann surface to a Grassmannian, Internat. J. Math. 5 (1994) 811 MR1298995
5 A Bertram, G Daskalopoulos, R Wentworth, Gromov invariants for holomorphic maps from Riemann surfaces to Grassmannians, J. Amer. Math. Soc. 9 (1996) 529 MR1320154
6 H l Chang, Y H Kiem, Poincaré invariants are Seiberg–Witten invariants, Geom. Topol. 17 (2013) 1149 MR3070521
7 E Cotterill, Geometry of curves with exceptional secant planes: linear series along the general curve, Math. Z. 267 (2011) 549 MR2776048
8 M Dürr, A Kabanov, C Okonek, Poincaré invariants, Topology 46 (2007) 225 MR2319736
9 G Ellingsrud, L Göttsche, M Lehn, On the cobordism class of the Hilbert scheme of a surface, J. Algebraic Geom. 10 (2001) 81 MR1795551
10 G Ellingsrud, M Lehn, On the irreducibility of the punctual quotient scheme of a surface, preprint (1997) arXiv:alg-geom/9704016
11 B Fantechi, L Göttsche, Riemann–Roch theorems and elliptic genus for virtually smooth schemes, Geom. Topol. 14 (2010) 83 MR2578301
12 I M Gessel, A combinatorial proof of the multivariable Lagrange inversion formula, J. Combin. Theory Ser. A 45 (1987) 178 MR894817
13 A Gholampour, A Sheshmani, S T Yau, Nested Hilbert schemes on surfaces : virtual fundamental class, Adv. Math. 365 (2020) 107046, 50 MR4064771
14 A Gholampour, R P Thomas, Degeneracy loci, virtual cycles and nested Hilbert schemes, I, Tunis. J. Math. 2 (2020) 633 MR4041285
15 L Göttsche, M Kool, Refined SU(3) Vafa–Witten invariants and modularity, Pure Appl. Math. Q. 14 (2018) 467 MR4047406
16 L Göttsche, M Kool, Virtual refinements of the Vafa–Witten formula, Comm. Math. Phys. 376 (2020) 1 MR4093873
17 L Göttsche, H Nakajima, K Yoshioka, Instanton counting and Donaldson invariants, J. Differential Geom. 80 (2008) 343 MR2472477
18 T Graber, R Pandharipande, Localization of virtual classes, Invent. Math. 135 (1999) 487 MR1666787
19 K Intriligator, Fusion residues, Modern Phys. Lett. A 6 (1991) 3543 MR1138873
20 D Johnson, D Oprea, R Pandharipande, Rationality of descendent series for Hilbert and Quot schemes of surfaces, Selecta Math. 27 (2021) MR4244329
21 T Kawai, K Yoshioka, String partition functions and infinite products, Adv. Theor. Math. Phys. 4 (2000) 397 MR1838446
22 Y H Kiem, J Li, Localizing virtual cycles by cosections, J. Amer. Math. Soc. 26 (2013) 1025 MR3073883
23 M Kool, Stable pair invariants of surfaces and Seiberg–Witten invariants, Q. J. Math. 67 (2016) 365 MR3556491
24 M Kool, V Shende, R P Thomas, A short proof of the Göttsche conjecture, Geom. Topol. 15 (2011) 397 MR2776848
25 T Laarakker, Monopole contributions to refined Vafa–Witten invariants, Geom. Topol. 24 (2020) 2781 MR4194304
26 P Le Barz, Sur une formule de Castelnuovo pour les espaces multisécants, Boll. Unione Mat. Ital. Sez. B Artic. Ric. Mat. 10 (2007) 381 MR2339448
27 J Lee, T H Parker, A structure theorem for the Gromov–Witten invariants of Kähler surfaces, J. Differential Geom. 77 (2007) 483 MR2362322
28 M Lehn, Chern classes of tautological sheaves on Hilbert schemes of points on surfaces, Invent. Math. 136 (1999) 157 MR1681097
29 M Levine, F Morel, Algebraic cobordism, Springer (2007) MR2286826
30 M Levine, R Pandharipande, Algebraic cobordism revisited, Invent. Math. 176 (2009) 63 MR2485880
31 J Li, Algebraic geometric interpretation of Donaldson’s polynomial invariants, J. Differential Geom. 37 (1993) 417 MR1205451
32 A Marian, On the intersection theory of Quot schemes and moduli of bundles with sections, J. Reine Angew. Math. 610 (2007) 13 MR2359849
33 A Marian, D Oprea, Counts of maps to Grassmannians and intersections on the moduli space of bundles, J. Differential Geom. 76 (2007) 155 MR2312051
34 A Marian, D Oprea, Virtual intersections on the Quot scheme and Vafa–Intriligator formulas, Duke Math. J. 136 (2007) 81 MR2271296
35 A Marian, D Oprea, R Pandharipande, The moduli space of stable quotients, Geom. Topol. 15 (2011) 1651 MR2851074
36 A Marian, D Oprea, R Pandharipande, Segre classes and Hilbert schemes of points, Ann. Sci. Éc. Norm. Supér. 50 (2017) 239 MR3621431
37 A Marian, D Oprea, R Pandharipande, The combinatorics of Lehn’s conjecture, J. Math. Soc. Japan 71 (2019) 299 MR3909922
38 A Marian, D Oprea, R Pandharipande, Higher rank Segre integrals over the Hilbert scheme of points, J. Eur. Math. Soc. (2021)
39 D Maulik, N Nekrasov, A Okounkov, R Pandharipande, Gromov–Witten theory and Donaldson–Thomas theory, I, Compos. Math. 142 (2006) 1263 MR2264664
40 D Maulik, N Nekrasov, A Okounkov, R Pandharipande, Gromov–Witten theory and Donaldson–Thomas theory, II, Compos. Math. 142 (2006) 1286 MR2264665
41 D Maulik, R Pandharipande, New calculations in Gromov–Witten theory, Pure Appl. Math. Q. 4 (2008) 469 MR2400883
42 D Maulik, R Pandharipande, R P Thomas, Curves on K3 surfaces and modular forms, J. Topol. 3 (2010) 937 MR2746343
43 R Pandharipande, A calculus for the moduli space of curves, from: "Algebraic geometry : Salt Lake City 2015" (editors T de Fernex, B Hassett, M Mustaţă, M Olsson, M Popa, R Thomas), Proc. Sympos. Pure Math. 97, Amer. Math. Soc. (2018) 459 MR3821159
44 R Pandharipande, A Pixton, Descendent theory for stable pairs on toric 3–folds, J. Math. Soc. Japan 65 (2013) 1337 MR3127827
45 R Pandharipande, A Pixton, Descendents on local curves: rationality, Compos. Math. 149 (2013) 81 MR3011879
46 R Pandharipande, A Pixton, Relations in the tautological ring of the moduli space of curves, Pure Appl. Math. Q. 17 (2021) 717 MR4257600
47 R Pandharipande, R P Thomas, Stable pairs and BPS invariants, J. Amer. Math. Soc. 23 (2010) 267 MR2552254
48 R Pandharipande, R P Thomas, The Katz–Klemm–Vafa conjecture for K3 surfaces, Forum Math. Pi 4 (2016) MR3508473
49 D Schultheis, Virtual invariants of Quot schemes over del Pezzo surfaces, PhD thesis, University of California, San Diego (2012)
50 J Shen, Cobordism invariants of the moduli space of stable pairs, J. Lond. Math. Soc. 94 (2016) 427 MR3556447
51 B Siebert, G Tian, On quantum cohomology rings of Fano manifolds and a formula of Vafa and Intriligator, Asian J. Math. 1 (1997) 679 MR1621570
52 R P Stanley, Catalan numbers, Cambridge Univ. Press (2015) MR3467982
53 Y Tanaka, R P Thomas, Vafa–Witten invariants for projective surfaces, II : Semistable case, Pure Appl. Math. Q. 13 (2017) 517 MR3882207
54 Y Tanaka, R P Thomas, Vafa–Witten invariants for projective surfaces, I : Stable case, J. Algebraic Geom. 29 (2020) 603 MR4158461
55 M Thaddeus, Stable pairs, linear systems and the Verlinde formula, Invent. Math. 117 (1994) 317 MR1273268
56 R P Thomas, A holomorphic Casson invariant for Calabi–Yau 3–folds, and bundles on K3 fibrations, J. Differential Geom. 54 (2000) 367 MR1818182
57 C Vafa, E Witten, A strong coupling test of S–duality, Nuclear Phys. B 431 (1994) 3 MR1305096
58 C Voisin, Segre classes of tautological bundles on Hilbert schemes of surfaces, Algebr. Geom. 6 (2019) 186 MR3914750
59 Z L Wang, Tautological integrals on symmetric products of curves, Acta Math. Sin. (Engl. Ser.) 32 (2016) 901 MR3520032
60 Z Wang, J Zhou, Generating series of intersection numbers on Hilbert schemes of points, Front. Math. China 12 (2017) 1247 MR3698424
61 E T Whittaker, G N Watson, A course of modern analysis, Cambridge Univ. Press (1996) MR1424469