CHARACTERISTIC CLASSES OF THE HILBERT SCHEMES OF POINTS ON NON-COMPACT SIMPLY-CONNECTED SURFACES

Marc A. Nieper-Wisskirchen (Germany)

Received September 28, 2007; Revised November 27, 2007

References:

[1] Michael F. Atiyah and Raoul Bott, The moment map and equivariant cohomology, Topology 23 (1984), 1-28. [2] Samuel Boissière and Marc Nieper-Wißkirchen, Generating series in the cohomology of Hilbert schemes of points on surfaces, to appear. [3] Samuel Boissière and Marc Nieper-Wißkirchen, Universal formulas for characteristic classes on the Hilbert schemes of points on surfaces, to appear. [4] Samuel Boissière, Chern classes of the tangent bundle on the Hilbert scheme of points on the affine plane, J. Algebraic Geom. 14(4) (2005), 761-787. [5] Dan Edidin and William Graham, Localization in equivariant intersection theory and the Bott residue formula, Am. J. Math. 120(3) (1998), 619-636. [6] J. Fogarty, Algebraic families on an algebraic surface, Am. J. Math. 90(2) (1968), 511-521. [7] Alexandre Grothendieck, Techniques de construction et théoremes d’existence en géométrie algébrique, IV, Les schemas de Hilbert, Sem. Bourbaki 13 (1960/61), No. 221, 1961. [8] I. Grojnowski, Instantons and affine algebras. I: The Hilbert scheme and vertex operators, Math. Res. Lett. 3(2) (1996), 275-291. [9] Friedrich Hirzebruch, Topological methods in algebraic geometry, Translation from the German and appendix one by R. L. E. Schwarzenberger, Appendix two by A. Borel, Reprint of the 2nd, Corr. print of the 3rd ed., Classics in Mathematics, Springer-Verlag, Berlin, 1995. [10] Ch. Krattenthaler, Operator methods and Lagrange inversion: a unified approach to Lagrange formulas, Trans. Am. Math. Soc. 305(2) (1988), 431-465. [11] Manfred Lehn, Chern classes of tautological sheaves on Hilbert schemes of points on surfaces, Invent. Math. 136(1) (1999), 157-207. [12] Wei-Ping Li, Zhenbo Qin and Weiqiang Wang, The cohomology rings of Hilbert schemes via Jack polynomials, Jacques Hurtubise et al., Algebraic Structures and Moduli Spaces, Proceedings of the CRM Workshop, Montréal, Canada, July 14-20, 2003, American Mathematical Society, Providence, RI, CRM Proceedings; and Lecture Notes 38 (2004), 249-258. [13] Ian Grant Macdonald, Symmetric functions and Hall polynomials, 2nd ed., Clarendon Press, Oxford, 1995 (English). [14] Hiraku Nakajima, Heisenberg algebra and Hilbert schemes of points on projective surfaces, Ann. Math. (2) 145(2) (1997), 379-388.

Keywords and phrases: Hilbert scheme, characteristic classes, equivariant cohomology, universal formulas, Lagrange-Good formula.