Download this article
 Download this article For screen
For printing
Recent Issues

Volume 30, 1 issue

Volume 29, 9 issues

Volume 28, 9 issues

Volume 27, 9 issues

Volume 26, 8 issues

Volume 25, 7 issues

Volume 24, 7 issues

Volume 23, 7 issues

Volume 22, 7 issues

Volume 21, 6 issues

Volume 20, 6 issues

Volume 19, 6 issues

Volume 18, 5 issues

Volume 17, 5 issues

Volume 16, 4 issues

Volume 15, 4 issues

Volume 14, 5 issues

Volume 13, 5 issues

Volume 12, 5 issues

Volume 11, 4 issues

Volume 10, 4 issues

Volume 9, 4 issues

Volume 8, 3 issues

Volume 7, 2 issues

Volume 6, 2 issues

Volume 5, 2 issues

Volume 4, 1 issue

Volume 3, 1 issue

Volume 2, 1 issue

Volume 1, 1 issue

The Journal
About the journal
Ethics and policies
Peer-review process
 
Submission guidelines
Submission form
Editorial board
 
Subscriptions
 
ISSN (electronic): 1364-0380
ISSN (print): 1465-3060
 
Author index
To appear
 
Other MSP journals
Multiple cover formulas for K3 geometries, wall-crossing, and Quot schemes

Georg Oberdieck

Geometry & Topology 28 (2024) 3221–3256
Bibliography
1 Y Bae, T H Buelles, Curves on K3 surfaces in divisibility 2, Forum Math. Sigma 9 (2021) MR4211942
2 J Bryan, The Donaldson–Thomas theory of K3 × E via the topological vertex, from: "Geometry of moduli" (editors J A Christophersen, K Ranestad), Abel Symp. 14, Springer (2018) 35 MR3968042
3 T H Buelles, Gromov–Witten classes of K3 surfaces, preprint (2019) arXiv:1912.00389
4 G Ellingsrud, L Göttsche, M Lehn, On the cobordism class of the Hilbert scheme of a surface, J. Algebraic Geom. 10 (2001) 81 MR1795551
5 B Fantechi, L Göttsche, Riemann–Roch theorems and elliptic genus for virtually smooth schemes, Geom. Topol. 14 (2010) 83 MR2578301
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 MR4157430
8 A Gholampour, A Sheshmani, S T Yau, Localized Donaldson–Thomas theory of surfaces, Amer. J. Math. 142 (2020) 405 MR4084159
9 D Huybrechts, Fourier–Mukai transforms in algebraic geometry, Oxford Univ. Press (2006) MR2244106
10 D Huybrechts, M Lehn, The geometry of moduli spaces of sheaves, E31, Vieweg & Sohn (1997) MR1450870
11 J W van Ittersum, G Oberdieck, A Pixton, Gromov–Witten theory of K3 surfaces and a Kaneko–Zagier equation for Jacobi forms, Selecta Math. 27 (2021) 64 MR4281261
12 S Katz, A Klemm, C Vafa, M-theory, topological strings and spinning black holes, Adv. Theor. Math. Phys. 3 (1999) 1445 MR1796683
13 T Kawai, K Yoshioka, String partition functions and infinite products, Adv. Theor. Math. Phys. 4 (2000) 397 MR1838446
14 Y H Kiem, J Li, Localizing virtual cycles by cosections, J. Amer. Math. Soc. 26 (2013) 1025 MR3073883
15 A Klemm, D Maulik, R Pandharipande, E Scheidegger, Noether–Lefschetz theory and the Yau–Zaslow conjecture, J. Amer. Math. Soc. 23 (2010) 1013 MR2669707
16 M Kool, R Thomas, Reduced classes and curve counting on surfaces, II : Calculations, Algebr. Geom. 1 (2014) 384 MR3238155
17 J Li, B Wu, Good degeneration of Quot-schemes and coherent systems, Comm. Anal. Geom. 23 (2015) 841 MR3385781
18 A Marian, D Oprea, Virtual intersections on the Quot scheme and Vafa–Intriligator formulas, Duke Math. J. 136 (2007) 81 MR2271296
19 D Maulik, R Pandharipande, R P Thomas, Curves on K3 surfaces and modular forms, J. Topol. 3 (2010) 937 MR2746343
20 A Neguţ, G Oberdieck, Q Yin, Motivic decompositions for the Hilbert scheme of points of a K3 surface, J. Reine Angew. Math. 778 (2021) 65 MR4308613
21 D Nesterov, Quasimaps to moduli spaces of sheaves, preprint (2021) arXiv:2111.11417
22 D Nesterov, Quasimaps to moduli spaces of sheaves on a K3 surface, preprint (2021) arXiv:2111.11425
23 D Nesterov, G Oberdieck, Elliptic curves in hyper-Kähler varieties, Int. Math. Res. Not. 2021 (2021) 2962 MR4218343
24 G Oberdieck, Gromov–Witten invariants of the Hilbert schemes of points of a K3 surface, Geom. Topol. 22 (2018) 323 MR3720346
25 G Oberdieck, On reduced stable pair invariants, Math. Z. 289 (2018) 323 MR3803792
26 G Oberdieck, Gromov–Witten theory of K3 × 1 and quasi-Jacobi forms, Int. Math. Res. Not. 2019 (2019) 4966 MR4009529
27 G Oberdieck, Gromov–Witten theory and Noether–Lefschetz theory for holomorphic-symplectic varieties, Forum Math. Sigma 10 (2022) MR4404412
28 G Oberdieck, Universality of descendent integrals over moduli spaces of stable sheaves on K3 surfaces, Symmetry Integrability Geom. Methods Appl. 18 (2022) 076 MR4495687
29 G Oberdieck, Marked relative invariants and GW/PT correspondences, Adv. Math. 439 (2024) 109472 MR4687909
30 G Oberdieck, Donaldson–Thomas theory of 𝕂 × 𝔼 in higher rank, in preparation
31 G Oberdieck, R Pandharipande, Curve counting on K3 ×E, the Igusa cusp form χ10, and descendent integration, from: "K3 surfaces and their moduli" (editors C Faber, G Farkas, G van der Geer), Progr. Math. 315, Birkhäuser (2016) 245 MR3524171
32 G Oberdieck, A Pixton, Holomorphic anomaly equations and the Igusa cusp form conjecture, Invent. Math. 213 (2018) 507 MR3827207
33 G Oberdieck, J Shen, Reduced Donaldson–Thomas invariants and the ring of dual numbers, Proc. Lond. Math. Soc. 118 (2019) 191 MR3898990
34 G Oberdieck, D Piyaratne, Y Toda, Donaldson–Thomas invariants of abelian threefolds and Bridgeland stability conditions, J. Algebraic Geom. 31 (2022) 13 MR4372406
35 A Okounkov, R Pandharipande, Virasoro constraints for target curves, Invent. Math. 163 (2006) 47 MR2208418
36 A Okounkov, R Pandharipande, The local Donaldson–Thomas theory of curves, Geom. Topol. 14 (2010) 1503 MR2679579
37 D Oprea, R Pandharipande, Quot schemes of curves and surfaces : virtual classes, integrals, Euler characteristics, Geom. Topol. 25 (2021) 3425 MR4372634
38 R Pandharipande, Counting elliptic plane curves with fixed j–invariant, Proc. Amer. Math. Soc. 125 (1997) 3471 MR1423328
39 R Pandharipande, A Pixton, Descendent theory for stable pairs on toric 3–folds, J. Math. Soc. Japan 65 (2013) 1337 MR3127827
40 R Pandharipande, R P Thomas, The Katz–Klemm–Vafa conjecture for K3 surfaces, Forum Math. Pi 4 (2016) MR3508473