Volume 15, issue 1 (2011)

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
Topological properties of Hilbert schemes of almost-complex four-manifolds II

Julien Grivaux

Geometry & Topology 15 (2011) 261–330
Bibliography
1 A Adem, J Leida, Y Ruan, Orbifolds and stringy topology, Cambridge Tracts in Math. 171, Cambridge Univ. Press (2007) MR2359514
2 M F Atiyah, F Hirzebruch, Analytic cycles on complex manifolds, Topology 1 (1962) 25 MR0145560
3 M F Atiyah, F Hirzebruch, The Riemann–Roch theorem for analytic embeddings, Topology 1 (1962) 151 MR0148084
4 A Beauville, Variétés Kähleriennes dont la première classe de Chern est nulle, J. Differential Geom. 18 (1983) MR730926
5 A Borel, J P Serre, Le théorème de Riemann–Roch, Bull. Soc. Math. France 86 (1958) 97 MR0116022
6 J Briançon, Description de $\mathrm{Hilb}^{n}C\{x,y\}$, Invent. Math. 41 (1977) 45 MR0457432
7 M A A de Cataldo, L Migliorini, The Douady space of a complex surface, Adv. Math. 151 (2000) 283 MR1758249
8 J Cheah, Cellular decompositions for nested Hilbert schemes of points, Pacific J. Math. 183 (1998) 39 MR1616606
9 W Chen, Y Ruan, A new cohomology theory of orbifold, Comm. Math. Phys. 248 (2004) 1 MR2104605
10 G Danila, Sur la cohomologie d'un fibré tautologique sur le schéma de Hilbert d'une surface, J. Algebraic Geom. 10 (2001) 247 MR1811556
11 S K Donaldson, Symplectic submanifolds and almost-complex geometry, J. Differential Geom. 44 (1996) 666 MR1438190
12 S K Donaldson, P B Kronheimer, The geometry of four-manifolds, Oxford Math. Monogr., Oxford Science Publ., The Clarendon Press, Oxford Univ. Press (1990) MR1079726
13 D Eisenbud, Commutative algebra with a view toward algebraic geometry, Graduate Texts in Math. 150, Springer (1995) MR1322960
14 G Ellingsrud, L Göttsche, M Lehn, On the cobordism class of the Hilbert scheme of a surface, J. Algebraic Geom. 10 (2001) 81 MR1795551
15 B Fantechi, L Göttsche, Orbifold cohomology for global quotients, Duke Math. J. 117 (2003) 197 MR1971293
16 J Fogarty, Algebraic families on an algebraic surface, Amer. J. Math 90 (1968) 511 MR0237496
17 L Göttsche, The Betti numbers of the Hilbert scheme of points on a smooth projective surface, Math. Ann. 286 (1990) 193 MR1032930
18 L Göttsche, Hilbert schemes of zero-dimensional subschemes of smooth varieties, Lecture Notes in Math. 1572, Springer (1994) MR1312161
19 L Göttsche, Hilbert schemes of points on surfaces, from: "Proceedings of the International Congress of Mathematicians, Vol. II (Beijing, 2002)" (editor T T Li), Higher Ed. Press (2002) 483 MR1957058
20 H Grauert, R Remmert, Theory of Stein spaces, Classics in Math., Springer (2004) MR2029201
21 J Grivaux, Topological properties of punctual Hilbert schemes of almost-complex fourfolds, to appear in Manuscripta Math. arXiv:1001.0114
22 J Grivaux, Quelques problèmes de géométrie complexe et presque complexe, PhD thesis, Université Pierre et Marie Curie (2009)
23 I Grojnowski, Instantons and affine algebras. I. The Hilbert scheme and vertex operators, Math. Res. Lett. 3 (1996) 275 MR1386846
24 A A Iarrobino, Punctual Hilbert schemes, Mem. Amer. Math. Soc. 10, no. 188 (1977) MR0485867
25 M Lehn, Chern classes of tautological sheaves on Hilbert schemes of points on surfaces, Invent. Math. 136 (1999) 157 MR1681097
26 M Lehn, C Sorger, Symmetric groups and the cup product on the cohomology of Hilbert schemes, Duke Math. J. 110 (2001) 345 MR1865244
27 M Lehn, C Sorger, The cup product of Hilbert schemes for $K3$ surfaces, Invent. Math. 152 (2003) 305 MR1974889
28 W P Li, Z Qin, W Wang, Generators for the cohomology ring of Hilbert schemes of points on surfaces, Internat. Math. Res. Notices (2001) 1057 MR1857595
29 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
30 W P Li, Z Qin, W Wang, Stability of the cohomology rings of Hilbert schemes of points on surfaces, J. Reine Angew. Math. 554 (2003) 217 MR1952174
31 B Malgrange, Division des distributions, from: "Séminaire Schwartz (1959/60), Exp. 25, Unicité du problème de Cauchy. Division des distributions", Faculté des Sciences de Paris (1960) 21 MR0124968
32 B Malgrange, Ideals of differentiable functions, Tata Institute of Fund. Research Studies in Math. 3, Tata Inst. of Fund. Research (1967) MR0212575
33 J Milnor, On the cobordism ring $\Omega^{*}$ and a complex analogue. I, Amer. J. Math. 82 (1960) 505 MR0119209
34 H Nakajima, Heisenberg algebra and Hilbert schemes of points on projective surfaces, Ann. of Math. $(2)$ 145 (1997) 379 MR1441880
35 H Nakajima, Lectures on Hilbert schemes of points on surfaces, Univ. Lecture Series 18, Amer. Math. Soc. (1999) MR1711344
36 S P Novikov, Topological invariance of rational classes of Pontrjagin, Dokl. Akad. Nauk SSSR 163 (1965) 298 MR0193644
37 Z Qin, W Wang, Hilbert schemes and symmetric products: a dictionary, from: "Orbifolds in mathematics and physics (Madison, WI, 2001)" (editors A Adem, J Morava, Y Ruan), Contemp. Math. 310, Amer. Math. Soc. (2002) 233 MR1950950
38 Y Ruan, The cohomology ring of crepant resolutions of orbifolds, from: "Gromov-Witten theory of spin curves and orbifolds" (editors T J Jarvis, T Kimura, A Vaintrob), Contemp. Math. 403, Amer. Math. Soc. (2006) 117 MR2234886
39 I Satake, On a generalization of the notion of manifold, Proc. Nat. Acad. Sci. USA 42 (1956) 359 MR0079769
40 I R Shafarevich, Basic algebraic geometry. 1. Varieties in projective space, Springer (1994) MR1328833
41 A S Tikhomirov, The variety of complete pairs of zero-dimensional subschemes of an algebraic surface, Izv. Ross. Akad. Nauk Ser. Mat. 61 (1997) 153 MR1609203
42 B Uribe, Orbifold cohomology of the symmetric product, Comm. Anal. Geom. 13 (2005) 113 MR2154668
43 C Voisin, On the Hilbert scheme of points of an almost complex fourfold, Ann. Inst. Fourier (Grenoble) 50 (2000) 689 MR1775365
44 C Voisin, On the punctual Hilbert scheme of a symplectic fourfold, from: "Symposium in Honor of C. H. Clemens (Salt Lake City, UT, 2000)" (editors A Bertram, J A Carlson, H Kley), Contemp. Math. 312, Amer. Math. Soc. (2002) 265 MR1941585