Volume 22, issue 1 (2018)

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

Volume 25
Issue 6, 2713–3256
Issue 5, 2167–2711
Issue 4, 1631–2166
Issue 3, 1087–1630
Issue 2, 547–1085
Issue 1, 1–546

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
Editorial Board
Editorial Interests
Subscriptions
 
Submission Guidelines
Submission Page
Policies for Authors
Ethics Statement
 
ISSN (electronic): 1364-0380
ISSN (print): 1465-3060
Author Index
To Appear
 
Other MSP Journals
Gromov–Witten invariants of the Hilbert schemes of points of a K3 surface

Georg Oberdieck

Geometry & Topology 22 (2018) 323–437
Bibliography
1 A Beauville, Counting rational curves on K3 surfaces, Duke Math. J. 97 (1999) 99 MR1682284
2 K Behrend, B Fantechi, The intrinsic normal cone, Invent. Math. 128 (1997) 45 MR1437495
3 J Bryan, N C Leung, The enumerative geometry of K3 surfaces and modular forms, J. Amer. Math. Soc. 13 (2000) 371 MR1750955
4 J Bryan, G Oberdieck, R Pandharipande, Q Yin, Curve counting on abelian surfaces and threefolds, preprint (2015) arXiv:1506.00841
5 K Chandrasekharan, Elliptic functions, 281, Springer (1985) MR808396
6 X Chen, A simple proof that rational curves on K3 are nodal, Math. Ann. 324 (2002) 71 MR1931759
7 C Ciliberto, A L Knutsen, On k–gonal loci in Severi varieties on general K3 surfaces and rational curves on hyperkähler manifolds, J. Math. Pures Appl. 101 (2014) 473 MR3179751
8 M Eichler, D Zagier, The theory of Jacobi forms, 55, Birkhäuser (1985) MR781735
9 C Faber, R Pandharipande, Relative maps and tautological classes, J. Eur. Math. Soc. 7 (2005) 13 MR2120989
10 C Faber, R Pandharipande, Tautological and non-tautological cohomology of the moduli space of curves, from: "Handbook of moduli, I" (editors G Farkas, I Morrison), Adv. Lect. Math. 24, International Press (2013) 293 MR3184167
11 W Fulton, Intersection theory, 2, Springer (1998) MR1644323
12 W Fulton, R Pandharipande, Notes on stable maps and quantum cohomology, from: "Algebraic geometry, 2" (editors J Kollár, R Lazarsfeld, D R Morrison), Proc. Sympos. Pure Math. 62, Amer. Math. Soc. (1997) 45 MR1492534
13 T Graber, Enumerative geometry of hyperelliptic plane curves, J. Algebraic Geom. 10 (2001) 725 MR1838977
14 V Gritsenko, K Hulek, G K Sankaran, Moduli of K3 surfaces and irreducible symplectic manifolds, from: "Handbook of moduli, I" (editors G Farkas, I Morrison), Adv. Lect. Math. 24, International Press (2013) 459 MR3184170
15 I Grojnowski, Instantons and affine algebras, I : The Hilbert scheme and vertex operators, Math. Res. Lett. 3 (1996) 275 MR1386846
16 J Harris, D Mumford, On the Kodaira dimension of the moduli space of curves, Invent. Math. 67 (1982) 23 MR664324
17 K Hori, S Katz, A Klemm, R Pandharipande, R Thomas, C Vafa, R Vakil, E Zaslow, Mirror symmetry, 1, Amer. Math. Soc. (2003) MR2003030
18 S Katz, A Klemm, R Pandharipande, On the motivic stable pairs invariants of K3 surfaces, from: "K3 surfaces and their moduli" (editors C Faber, G Farkas, G van der Geer), Progr. Math. 315, Birkhäuser (2016) 111 MR3524167
19 T Kawai, K Yoshioka, String partition functions and infinite products, Adv. Theor. Math. Phys. 4 (2000) 397 MR1838446
20 Y H Kiem, J Li, Localizing virtual cycles by cosections, J. Amer. Math. Soc. 26 (2013) 1025 MR3073883
21 M Lehn, Chern classes of tautological sheaves on Hilbert schemes of points on surfaces, Invent. Math. 136 (1999) 157 MR1681097
22 M Lehn, Lectures on Hilbert schemes, from: "Algebraic structures and moduli spaces" (editors J Hurtubise, E Markman), CRM Proc. Lecture Notes 38, Amer. Math. Soc. (2004) 1 MR2095898
23 M Lehn, C Sorger, The cup product of Hilbert schemes for K3 surfaces, Invent. Math. 152 (2003) 305 MR1974889
24 W p Li, Z Qin, W Wang, Vertex algebras and the cohomology ring structure of Hilbert schemes of points on surfaces, Math. Ann. 324 (2002) 105 MR1931760
25 A Libgober, Elliptic genera, real algebraic varieties and quasi-Jacobi forms, from: "Topology of stratified spaces" (editors G Friedman, E Hunsicker, A Libgober, L Maxim), Math. Sci. Res. Inst. Publ. 58, Cambridge Univ. Press (2011) 95 MR2796409
26 D Maulik, A Oblomkov, Donaldson–Thomas theory of 𝒜n × P1, Compos. Math. 145 (2009) 1249 MR2551996
27 D Maulik, A Oblomkov, Quantum cohomology of the Hilbert scheme of points on 𝒜n–resolutions, J. Amer. Math. Soc. 22 (2009) 1055 MR2525779
28 D Maulik, A Okounkov, Quantum groups and quantum cohomology, preprint (2012) arXiv:1211.1287
29 D Maulik, R Pandharipande, Gromov–Witten theory and Noether–Lefschetz theory, from: "A celebration of algebraic geometry" (editors B Hassett, J McKernan, J Starr, R Vakil), Clay Math. Proc. 18, Amer. Math. Soc. (2013) 469 MR3114953
30 D Maulik, R Pandharipande, R P Thomas, Curves on K3 surfaces and modular forms, J. Topol. 3 (2010) 937 MR2746343
31 H Nakajima, Heisenberg algebra and Hilbert schemes of points on projective surfaces, Ann. of Math. 145 (1997) 379 MR1441880
32 H Nakajima, Lectures on Hilbert schemes of points on surfaces, 18, Amer. Math. Soc. (1999) MR1711344
33 G Oberdieck, A Serre derivative for even weight Jacobi forms, preprint (2012) arXiv:1209.5628
34 G Oberdieck, The enumerative geometry of the Hilbert schemes of points of a K3 surface, PhD thesis, ETH Zürich (2015)
35 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
36 A Okounkov, R Pandharipande, Quantum cohomology of the Hilbert scheme of points in the plane, Invent. Math. 179 (2010) 523 MR2587340
37 R Pandharipande, R P Thomas, The Katz–Klemm–Vafa conjecture for K3 surfaces, Forum Math. Pi 4 (2016) MR3508473
38 D Pontoni, Quantum cohomology of Hilb2(1 × 1) and enumerative applications, Trans. Amer. Math. Soc. 359 (2007) 5419 MR2327036
39 J P Pridham, Semiregularity as a consequence of Goodwillie’s theorem, preprint (2012) arXiv:1208.3111
40 S C F Rose, Counting hyperelliptic curves on an Abelian surface with quasi-modular forms, Commun. Number Theory Phys. 8 (2014) 243 MR3271176
41 T Schürg, B Toën, G Vezzosi, Derived algebraic geometry, determinants of perfect complexes, and applications to obstruction theories for maps and complexes, J. Reine Angew. Math. 702 (2015) 1 MR3341464
42 S T Yau, E Zaslow, BPS states, string duality, and nodal curves on K3, Nuclear Phys. B 471 (1996) 503 MR1398633