
Generating series of intersection numbers on Hilbert schemes of points
Zhilan WANG, Jian ZHOU
Front. Math. China ›› 2017, Vol. 12 ›› Issue (5) : 1247-1264.
Generating series of intersection numbers on Hilbert schemes of points
We compute some generating series of integrals related to tautological bundles on Hilbert schemes of points on surfaces S[n], including the intersection numbers of two Chern classes of tautological bundles, and the Euler characteristics of Λ_yTS[n]. We also propose some related conjectures, including an equivariant version of Lehn’s conjecture.
Hilbert scheme / tautological sheaf / intersection number
[1] |
AtiyahM F, BottR. The moment map and equivariant cohomology. Topology, 1984, 23(1): 1–28
CrossRef
Google scholar
|
[2] |
BorisovL, LibgoberA. McKay correspondence for elliptic genera. Ann of Math, 2005, 1521–1569
CrossRef
Google scholar
|
[3] |
EllingsrudG, GöttscheL, LehnM. On the cobordism class of the Hilbert scheme of a surface. J Algebraic Geom, 2001, 10: 81–100
|
[4] |
EllingsrudG, StrømmeS A. On the homology of the Hilbert scheme of points in the plane. Invent Math, 1987, 87(2): 343–352
CrossRef
Google scholar
|
[5] |
GöttscheL. The Betti numbers of the Hilbert scheme of points on a smooth projective surface. Math Ann, 1990, 286(1): 193–207
CrossRef
Google scholar
|
[6] |
GöttscheL, SoergelW. Perverse sheaves and the cohomology of Hilbert schemes of smooth algebraic surfaces. Math Ann, 1993, 296(1): 235–245
CrossRef
Google scholar
|
[7] |
IqbalA, NazirS, RazaZ, SaleemZ. Generalizations of Nekrasov-Okounkov identity. Ann Comb, 2012, 16(4): 745–753
CrossRef
Google scholar
|
[8] |
LehnM. Chern classes of tautological sheaves on Hilbert schemes of points on surfaces. Invent Math, 1999, 136(1): 157–207
CrossRef
Google scholar
|
[9] |
LiJ, LiuK, ZhouJ. Topological string partition functions as equivariant indices. Asian J Math, 2006, 10(1): 81–114
CrossRef
Google scholar
|
[10] |
LiuK, YanC, ZhouJ. Hirzebruch χy genera of the Hilbert schemes of surfaces by localization formula. Sci China Ser A-Math, 2002, 45(4):420–431
CrossRef
Google scholar
|
[11] |
MacdonaldI G. Symmetric Functions and Hall Polynomials. Oxford: Oxford Univ Press, 1998
|
[12] |
MarianA, OpreaD, PandharipandeR. Segre classes and Hilbert schemes of points. arXiv: 1507.00688
|
[13] |
NakajimaH. Heisenberg algebra and Hilbert schemes of points on projective surfaces. Ann of Math, 1997, 145(2): 379–388
CrossRef
Google scholar
|
[14] |
NakajimaH. Lectures on Hilbert Schemes of Points on Surfaces. University Lecture Series, Vol 18. Providence: Amer Math Soc, 1999
|
[15] |
SloaneN J. The On-line Encyclopedia of Integer Sequences. https://oeis.org
|
[16] |
TikhomirovA. Standard bundles on a Hilbert scheme of points on a surface. In: Tikhomirov A, Tyurin A, eds. Algebraic Geometry and its Applications: Proceedings of the 8th Algebraic Geometry Conference, Yaroslavl 1992. Aspects of Mathematics, Vol 25. Wiesbaden: Vieweg+Teubner Verlag, 1994, 183–203
CrossRef
Google scholar
|
[17] |
VafaC, WittenE. A strong coupling test of S-duality. Nuclear Phys, 1994, 431(1): 3–77
CrossRef
Google scholar
|
[18] |
WangZ. Tautological Sheaves on Hilbert Schemes. Ph D Thesis. Tsinghua University, Beijing, 2014
|
[19] |
19. Wang Z, Zhou J. Tautological sheaves on Hilbert schemes of points. J Algebraic Geom, 2014, 23(4): 669–692
CrossRef
Google scholar
|
/
〈 |
|
〉 |