Geometry & Topology Volume 21, issue 5 (2017)

Download this article
	For screen
	For printing

Recent Issues

The Journal

About the journal

Ethics and policies

Peer-review process

Submission guidelines

Submission form

Editorial board

Subscriptions

ISSN (electronic): 1364-0380

ISSN (print): 1465-3060

Author index

To appear

Other MSP journals

Tautological integrals on curvilinear Hilbert schemes

Gergely Bérczi

Geometry & Topology 21 (2017) 2897–2944

DOI: 10.2140/gt.2017.21.2897

Bibliography

1	M F Atiyah, R Bott, The moment map and equivariant cohomology, Topology 23 (1984) 1 MR721448
2	G Bérczi, Thom polynomials of Morin singularities and the Green–Griffiths–Lang conjecture, preprint (2010) arXiv:1011.4710
3	G Bérczi, B Doran, T Hawes, F Kirwan, Geometric invariant theory for graded unipotent groups and applications, preprint (2016) arXiv:1601.00340
4	G Bérczi, B Doran, T Hawes, F Kirwan, Projective completions of graded unipotent quotients, preprint (2016) arXiv:1607.04181
5	G Bérczi, F Kirwan, Graded unipotent groups and Grosshans theory, preprint (2015) arXiv:1511.06983
6	G Bérczi, A Szenes, Tautological integrals on Hilbert schemes and counting singular hypersurfaces, in preparation
7	G Bérczi, A Szenes, Thom polynomials of Morin singularities, Ann. of Math. 175 (2012) 567 MR2877067
8	N Berline, E Getzler, M Vergne, Heat kernels and Dirac operators, 298, Springer (2004) MR2273508
9	N Berline, M Vergne, Zéros d’un champ de vecteurs et classes caractéristiques équivariantes, Duke Math. J. 50 (1983) 539 MR705039
10	R Bott, L W Tu, Differential forms in algebraic topology, 82, Springer (1982) MR658304
11	J P Demailly, Algebraic criteria for Kobayashi hyperbolic projective varieties and jet differentials, from: "Algebraic geometry" (editors J Kollár, R Lazarsfeld, D R Morrison), Proc. Sympos. Pure Math. 62, Amer. Math. Soc. (1997) 285 MR1492539
12	M Duflo, M Vergne, Orbites coadjointes et cohomologie équivariante, from: "The orbit method in representation theory" (editors M Duflo, N V Pedersen, M Vergne), Progr. Math. 82, Birkhäuser (1990) 11 MR1095340
13	D Edidin, W Graham, Characteristic classes in the Chow ring, J. Algebraic Geom. 6 (1997) 431 MR1487222
14	D Eisenbud, Commutative algebra, 150, Springer (1995) MR1322960
15	G Ellingsrud, L Göttsche, M Lehn, On the cobordism class of the Hilbert scheme of a surface, J. Algebraic Geom. 10 (2001) 81 MR1795551
16	L M Fehér, R Rimányi, Thom series of contact singularities, Ann. of Math. 176 (2012) 1381 MR2979854
17	W Fulton, Intersection theory, 2, Springer (1984) MR732620
18	W Fulton, Equivariant cohomology in algebraic geometry, Eilenberg lectures (2007)
19	T Gaffney, The Thom polynomial of Σ¹¹¹¹, from: "Singularities, 1" (editor P Orlik), Proc. Sympos. Pure Math. 40, Amer. Math. Soc. (1983) 399 MR713080
20	L Göttsche, A conjectural generating function for numbers of curves on surfaces, Comm. Math. Phys. 196 (1998) 523 MR1645204
21	M Green, P Griffiths, Two applications of algebraic geometry to entire holomorphic mappings, from: "The Chern Symposium 1979" (editors H H Wu, S Kobayashi, I M Singer, A Weinstein, J Wolf), Springer (1980) 41 MR609557
22	M É Kazarian, Characteristic classes of singularity theory, from: "The Arnold–Gelfand mathematical seminars" (editors V I Arnold, I M Gelfand, V S Retakh, M Smirnov), Birkhäuser (1997) 325 MR1429898
23	M È Kazarian, Multisingularities, cobordisms, and enumerative geometry, Uspekhi Mat. Nauk 58 (2003) 29 MR2042262
24	S Kleiman, R Piene, Enumerating singular curves on surfaces, from: "Algebraic geometry : Hirzebruch 70" (editors P Pragacz, M Szurek, J Wiśniewski), Contemp. Math. 241, Amer. Math. Soc. (1999) 209 MR1718146
25	M Kool, V Shende, R P Thomas, A short proof of the Göttsche conjecture, Geom. Topol. 15 (2011) 397 MR2776848
26	M Lehn, Chern classes of tautological sheaves on Hilbert schemes of points on surfaces, Invent. Math. 136 (1999) 157 MR1681097
27	J Li, Zero dimensional Donaldson–Thomas invariants of threefolds, Geom. Topol. 10 (2006) 2117 MR2284053
28	A K Liu, Family blowup formula, admissible graphs and the enumeration of singular curves, I, J. Differential Geom. 56 (2000) 381 MR1868322
29	A Marian, D Oprea, R Pandharipande, Segre classes and Hilbert schemes of points, preprint (2015) arXiv:1507.00688
30	V Mathai, D Quillen, Superconnections, Thom classes, and equivariant differential forms, Topology 25 (1986) 85 MR836726
31	E Miller, B Sturmfels, Combinatorial commutative algebra, 227, Springer (2005) MR2110098
32	H Nakajima, Heisenberg algebra and Hilbert schemes of points on projective surfaces, Ann. of Math. 145 (1997) 379 MR1441880
33	J Rennemo, Universal polynomials for tautological integrals on Hilbert schemes, Geom. Topol. 21 (2017) 253 MR3608714
34	W Rossmann, Equivariant multiplicities on complex varieties, from: "Orbites unipotentes et représentations, III", Astérisque 173–174, Société Mathématique de France (1989) 313 MR1021516
35	A Szenes, Iterated residues and multiple Bernoulli polynomials, Internat. Math. Res. Notices (1998) 937 MR1653791
36	Y J Tzeng, A proof of the Göttsche–Yau–Zaslow formula, J. Differential Geom. 90 (2012) 439 MR2916043
37	M Vergne, Polynômes de Joseph et représentation de Springer, Ann. Sci. École Norm. Sup. 23 (1990) 543 MR1072817