Volume 15, issue 1 (2011)

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A short proof of the Göttsche conjecture

Martijn Kool, Vivek Shende and Richard P Thomas

Geometry & Topology 15 (2011) 397–406
Bibliography
1 A Beauville, Counting rational curves on $K3$ surfaces, Duke Math. J. 97 (1999) 99 MR1682284
2 J Bryan, N C Leung, Generating functions for the number of curves on abelian surfaces, Duke Math. J. 99 (1999) 311 MR1708022
3 J Bryan, N C Leung, The enumerative geometry of $K3$ surfaces and modular forms, J. Amer. Math. Soc. 13 (2000) 371 MR1750955
4 L Caporaso, J Harris, Counting plane curves of any genus, Invent. Math. 131 (1998) 345 MR1608583
5 Y Choi, Enumerative geometry of plane curves, PhD thesis, University of California, Riverside (1999)
6 P Di Francesco, C Itzykson, Quantum intersection rings, from: "The moduli space of curves (Texel Island, 1994)", Progr. Math. 129, Birkhäuser (1995) 81 MR1363054
7 S Diaz, J Harris, Ideals associated to deformations of singular plane curves, Trans. Amer. Math. Soc. 309 (1988) 433 MR961600
8 G Ellingsrud, L Göttsche, M Lehn, On the cobordism class of the Hilbert scheme of a surface, J. Algebraic Geom. 10 (2001) 81 MR1795551
9 S Fomin, G Mikhalkin, Labeled floor diagrams for plane curves arXiv:0906.3828
10 L Göttsche, A conjectural generating function for numbers of curves on surfaces, Comm. Math. Phys. 196 (1998) 523 MR1645204
11 T Kawai, K Yoshioka, String partition functions and infinite products, Adv. Theor. Math. Phys. 4 (2000) 397 MR1838446
12 M È Kazarian, Multisingularities, cobordisms, and enumerative geometry, Russian Math. Surveys 58 (2003) 665 MR2042262
13 S L Kleiman, R Piene, Enumerating singular curves on surfaces, from: "Algebraic geometry: Hirzebruch 70 (Warsaw, 1998)" (editors P Pragacz, M Szurek, J Wiśniewski), Contemp. Math. 241, Amer. Math. Soc. (1999) 209 MR1718146
14 S L Kleiman, R Piene, Node polynomials for families: methods and applications, Math. Nachr. 271 (2004) 69 MR2068884
15 M Kool, R P Thomas, Reduced classes and curve counting on surfaces, in preparation
16 L D Tráng, C P Ramanujam, The invariance of Milnor's number implies the invariance of the topological type, Amer. J. Math. 98 (1976) 67 MR0399088
17 A K Liu, The algebraic proof of the universality theorem arXiv:math.AG/0402045
18 A K Liu, Family blowup formula, admissible graphs and the enumeration of singular curves. I, J. Differential Geom. 56 (2000) 381 MR1868322
19 D Maulik, N Nekrasov, A Okounkov, R Pandharipande, Gromov–Witten theory and Donaldson–Thomas theory. I, Compos. Math. 142 (2006) 1263 MR2264664
20 D Maulik, R Pandharipande, R P Thomas, Curves on $K3$ surfaces and modular forms, J. Topol. 3 (2010) 937
21 R Pandharipande, R P Thomas, Curve counting via stable pairs in the derived category, Invent. Math. 178 (2009) 407 MR2545686
22 R Pandharipande, R P Thomas, Stable pairs and BPS invariants, J. Amer. Math. Soc. 23 (2010) 267 MR2552254
23 Z Ran, Enumerative geometry of singular plane curves, Invent. Math. 97 (1989) 447 MR1005002
24 V Shende, Hilbert schemes of points on a locally planar curve and the Severi strata of its versal deformation arXiv:1009.0914
25 B Teissier, Résolution simultanée: I – Familles de courbes, from: "Séminaire sur les Singularités des Surfaces" (editors M Demazure, H C Pinkham, B Teissier), Lecture Notes in Math. 777, Springer (1980) 1 MR579026
26 Y Tzeng, A proof of the Göttsche–Yau–Zaslow formula arXiv:1009.5371
27 I Vainsencher, Enumeration of $n$–fold tangent hyperplanes to a surface, J. Algebraic Geom. 4 (1995) 503 MR1325790
28 S T Yau, E Zaslow, BPS states, string duality, and nodal curves on $K3$, Nuclear Phys. B 471 (1996) 503 MR1398633