Volume 22, issue 1 (2018)

Download this article
Download this article For screen
For printing
Recent Issues

Volume 26
Issue 7, 2855–3306
Issue 6, 2405–2853
Issue 5, 1907–2404
Issue 4, 1435–1905
Issue 3, 937–1434
Issue 2, 477–936
Issue 1, 1–476

Volume 25, 7 issues

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
Editorial Procedure
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
Equivariant characteristic classes of external and symmetric products of varieties

Laurenţiu Maxim and Jörg Schürmann

Geometry & Topology 22 (2018) 471–515
Bibliography
1 M F Atiyah, Power operations in K–theory, Quart. J. Math. Oxford Ser. 17 (1966) 165 MR0202130
2 M F Atiyah, I M Singer, The index of elliptic operators, III, Ann. of Math. 87 (1968) 546 MR0236952
3 P Baum, J L Brylinski, R MacPherson, Cohomologie équivariante délocalisée, C. R. Acad. Sci. Paris Sér. I Math. 300 (1985) 605 MR791098
4 P Baum, A Connes, Chern character for discrete groups, from: "A fête of topology" (editors Y Matsumoto, T Mizutani, S Morita), Academic Press (1988) 163 MR928402
5 P Baum, W Fulton, R MacPherson, Riemann–Roch for singular varieties, Inst. Hautes Études Sci. Publ. Math. 45 (1975) 101 MR0412190
6 P Baum, W Fulton, G Quart, Lefschetz–Riemann–Roch for singular varieties, Acta Math. 143 (1979) 193 MR549774
7 D Bergh, The binomial theorem and motivic classes of universal quasi-split tori, preprint (2014) arXiv:1409.5410
8 L Borisov, A Libgober, McKay correspondence for elliptic genera, Ann. of Math. 161 (2005) 1521 MR2180406
9 J P Brasselet, J Schürmann, S Yokura, Hirzebruch classes and motivic Chern classes for singular spaces, J. Topol. Anal. 2 (2010) 1 MR2646988
10 S Cappell, L Maxim, T Ohmoto, J Schürmann, S Yokura, Characteristic classes of Hilbert schemes of points via symmetric products, Geom. Topol. 17 (2013) 1165 MR3070522
11 S E Cappell, L G Maxim, J Schürmann, J L Shaneson, Equivariant characteristic classes of singular complex algebraic varieties, Comm. Pure Appl. Math. 65 (2012) 1722 MR2982640
12 S E Cappell, L Maxim, J Schürmann, J L Shaneson, S Yokura, Characteristic classes of symmetric products of complex quasi-projective varieties, J. Reine Angew. Math. 728 (2017) 35 MR3668990
13 P Deligne, Catégories tensorielles, Mosc. Math. J. 2 (2002) 227 MR1944506
14 D Edidin, Riemann–Roch for Deligne–Mumford stacks, from: "A celebration of algebraic geometry" (editors B Hassett, J McKernan, J Starr, R Vakil), Clay Math. Proc. 18, Amer. Math. Soc. (2013) 241 MR3114943
15 D Edidin, W Graham, Riemann–Roch for equivariant Chow groups, Duke Math. J. 102 (2000) 567 MR1756110
16 C Farsi, M J Pflaum, C Seaton, Stratifications of inertia spaces of compact Lie group actions, J. Singul. 13 (2015) 107 MR3343617
17 E Getzler, Mixed Hodge structures of configuration spaces, preprint (1995) arXiv:alg-geom/9510018
18 E Gorsky, Adams operations and power structures, Mosc. Math. J. 9 (2009) 305 MR2568440
19 F Heinloth, A note on functional equations for zeta functions with values in Chow motives, Ann. Inst. Fourier (Grenoble) 57 (2007) 1927 MR2377891
20 F Hirzebruch, D Zagier, The Atiyah–Singer theorem and elementary number theory, 3, Publish or Perish (1974) MR0650832
21 T Kawasaki, The index of elliptic operators over V –manifolds, Nagoya Math. J. 84 (1981) 135 MR641150
22 A Krug, Remarks on the derived McKay correspondence for Hilbert schemes of points and tautological bundles, preprint (2016) arXiv:1612.04348
23 I G Macdonald, The Poincaré polynomial of a symmetric product, Proc. Cambridge Philos. Soc. 58 (1962) 563 MR0143204
24 I G Macdonald, Symmetric functions and Hall polynomials, Clarendon (1979) MR553598
25 R D MacPherson, Chern classes for singular algebraic varieties, Ann. of Math. 100 (1974) 423 MR0361141
26 L Maxim, M Saito, J Schürmann, Symmetric products of mixed Hodge modules, J. Math. Pures Appl. 96 (2011) 462 MR2843222
27 L Maxim, J Schürmann, Twisted genera of symmetric products, Selecta Math. 18 (2012) 283 MR2891866
28 L Maxim, J Schürmann, Plethysm and cohomology representations of external and symmetric products, preprint (2016) arXiv:1602.06546
29 S Meinhardt, M Reineke, Donaldson–Thomas invariants versus intersection cohomology of quiver moduli, J. Reine Angew. Math. (2017)
30 B Moonen, Das Lefschetz–Riemann–Roch–Theorem für singuläre Varietäten, Dissertation, Rheinische Friedrich-Wilhelms-Universität Bonn (1978) MR544020
31 M V Nori, The Hirzebruch–Riemann–Roch theorem, Michigan Math. J. 48 (2000) 473 MR1786501
32 T Ohmoto, Equivariant Chern classes of singular algebraic varieties with group actions, Math. Proc. Cambridge Philos. Soc. 140 (2006) 115 MR2197579
33 T Ohmoto, Generating functions of orbifold Chern classes, I : Symmetric products, Math. Proc. Cambridge Philos. Soc. 144 (2008) 423 MR2405899
34 Z Qin, W Wang, Hilbert schemes and symmetric products: a dictionary, from: "Orbifolds in mathematics and physics" (editors A Adem, J Morava, Y Ruan), Contemp. Math. 310, Amer. Math. Soc. (2002) 233 MR1950950
35 L Scala, Cohomology of the Hilbert scheme of points on a surface with values in representations of tautological bundles, Duke Math. J. 150 (2009) 211 MR2569613
36 L Scala, Some remarks on tautological sheaves on Hilbert schemes of points on a surface, Geom. Dedicata 139 (2009) 313 MR2481854
37 J Schürmann, A general construction of partial Grothendieck transformations, preprint (2002) arXiv:math/0209299
38 J Schürmann, Characteristic classes of mixed Hodge modules, from: "Topology of stratified spaces" (editors G Friedman, E Hunsicker, A Libgober, L Maxim), Math. Sci. Res. Inst. Publ. 58, Cambridge Univ. Press (2011) 419 MR2796417
39 B Toen, Théorèmes de Riemann–Roch pour les champs de Deligne–Mumford, K–Theory 18 (1999) 33 MR1710187
40 W Wang, Equivariant K–theory, wreath products, and Heisenberg algebra, Duke Math. J. 103 (2000) 1 MR1758236
41 W Wang, J Zhou, Orbifold Hodge numbers of the wreath product orbifolds, J. Geom. Phys. 38 (2001) 152 MR1823666
42 Z Wang, J Zhou, Tautological sheaves on Hilbert schemes of points, J. Algebraic Geom. 23 (2014) 669 MR3263664
43 J Zhou, Delocalized equivariant coholomogy of symmetric products, preprint (1999) arXiv:math/9910028