Geometry & Topology Volume 15, issue 1 (2011)

Download this article
	For screen
	For printing

Recent Issues

The Journal

Submission Guidelines

Submission Page

Policies for Authors

Ethics Statement

ISSN 1364-0380 (online)

ISSN 1465-3060 (print)

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

DOI: 10.2140/gt.2011.15.261

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