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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