| [1] | Atiyah, M. F., \(K\)-theory, v+166+xlix pp. (1967), W. A. Benjamin, Inc., New York-Amsterdam ·Zbl 0159.53302 |
| [2] | A’Campo, Norbert, Tresses, monodromie et le groupe symplectique, Comment. Math. Helv., 318-327 (1979) ·Zbl 0441.32004 ·doi:10.1007/BF02566275 |
| [3] | Baum, Paul, Riemann-Roch for singular varieties, Inst. Hautes \'{E}tudes Sci. Publ. Math., 101-145 (1975) ·Zbl 0332.14003 |
| [4] | Beauville, Arnaud, Spectral curves and the generalised theta divisor, J. Reine Angew. Math., 169-179 (1989) ·Zbl 0666.14015 ·doi:10.1515/crll.1989.398.169 |
| [5] | Be\u{\i }linson, A. A., Analysis and topology on singular spaces, I. Faisceaux pervers, Ast\'{e}risque, 5-171 (1981), Soc. Math. France, Paris |
| [6] | Borel, Armand, Density properties for certain subgroups of semi-simple groups without compact components, Ann. of Math. (2), 179-188 (1960) ·Zbl 0094.24901 ·doi:10.2307/1970150 |
| [7] | Chuang, W.-Y., Moduli spaces. BPS states and the \(P=W\) conjecture, London Math. Soc. Lecture Note Ser., 132-150 (2014), Cambridge Univ. Press, Cambridge ·Zbl 1320.14057 |
| [8] | de Cataldo, Mark Andrea, Geometry of moduli spaces and representation theory. Perverse sheaves and the topology of algebraic varieties, IAS/Park City Math. Ser., 1-58 (2017), Amer. Math. Soc., Providence, RI ·Zbl 1439.14060 |
| [9] | de Cataldo, Mark Andrea A., Hodge-theoretic splitting mechanisms for projective maps, J. Singul., 134-156 (2013) ·Zbl 1317.14045 ·doi:10.5427/jsing.2013.7h |
| [10] | M. A. de Cataldo, Perverse Leray filtration and specialization with applications to the Hitchin morphism, to appear in Math. Proc. Cambridge Phil. Soc., arXiv:2102.02264, 2021. |
| [11] | de Cataldo, Mark Andrea A., Topology of Hitchin systems and Hodge theory of character varieties: the case \(A_1\), Ann. of Math. (2), 1329-1407 (2012) ·Zbl 1375.14047 ·doi:10.4007/annals.2012.175.3.7 |
| [12] | de Cataldo, Mark Andrea A., Exchange between perverse and weight filtration for the Hilbert schemes of points of two surfaces, J. Singul., 23-38 (2013) ·Zbl 1304.14011 ·doi:10.5427/jsing.2013.7c |
| [13] | de Cataldo, Mark Andrea A., The perverse filtration for the Hitchin fibration is locally constant, Pure Appl. Math. Q., 1441-1464 (2020) ·Zbl 1462.53062 ·doi:10.4310/PAMQ.2020.v16.n5.a4 |
| [14] | de Cataldo, Mark Andrea A., The Chow groups and the motive of the Hilbert scheme of points on a surface, J. Algebra, 824-848 (2002) ·Zbl 1033.14004 ·doi:10.1006/jabr.2001.9105 |
| [15] | de Cataldo, Mark Andrea A., The Hodge theory of algebraic maps, Ann. Sci. \'{E}cole Norm. Sup. (4), 693-750 (2005) ·Zbl 1094.14005 ·doi:10.1016/j.ansens.2005.07.001 |
| [16] | de Cataldo, Mark Andrea A., The decomposition theorem, perverse sheaves and the topology of algebraic maps, Bull. Amer. Math. Soc. (N.S.), 535-633 (2009) ·Zbl 1181.14001 ·doi:10.1090/S0273-0979-09-01260-9 |
| [17] | de Cataldo, Mark Andrea A., Algebraic geometry-Seattle 2005. Part 2. Hodge-theoretic aspects of the decomposition theorem, Proc. Sympos. Pure Math., 489-504 (2009), Amer. Math. Soc., Providence, RI ·Zbl 1207.14016 ·doi:10.1090/pspum/080.2/2483945 |
| [18] | Deligne, Pierre, Motives. D\'{e}compositions dans la cat\'{e}gorie d\'{e}riv\'{e}e, Proc. Sympos. Pure Math., 115-128 (1991), Amer. Math. Soc., Providence, RI ·Zbl 0809.18008 ·doi:10.1090/pspum/055.1/1265526 |
| [19] | Donagi, Ron, Birational algebraic geometry. Nilpotent cones and sheaves on \(K3\) surfaces, Contemp. Math., 51-61 (1996), Amer. Math. Soc., Providence, RI ·Zbl 0907.32004 ·doi:10.1090/conm/207/02719 |
| [20] | Fulton, William, Intersection theory, Ergebnisse der Mathematik und ihrer Grenzgebiete (3) [Results in Mathematics and Related Areas (3)], xi+470 pp. (1984), Springer-Verlag, Berlin ·Zbl 0885.14002 ·doi:10.1007/978-3-662-02421-8 |
| [21] | G\"{o}ttsche, Lothar, The Betti numbers of the Hilbert scheme of points on a smooth projective surface, Math. Ann., 193-207 (1990) ·Zbl 0679.14007 ·doi:10.1007/BF01453572 |
| [22] | G\"{o}ttsche, Lothar, Perverse sheaves and the cohomology of Hilbert schemes of smooth algebraic surfaces, Math. Ann., 235-245 (1993) ·Zbl 0789.14002 ·doi:10.1007/BF01445104 |
| [23] | Harder, Andrew, \(P = W\) for Lagrangian fibrations and degenerations of hyper-K\"{a}hler manifolds, Forum Math. Sigma, Paper No. e50, 6 pp. (2021) ·Zbl 1467.14101 ·doi:10.1017/fms.2021.31 |
| [24] | Hausel, Tam\'{a}s, Mixed Hodge polynomials of character varieties, Invent. Math., 555-624 (2008) ·Zbl 1213.14020 ·doi:10.1007/s00222-008-0142-x |
| [25] | Hausel, Tam\'{a}s, Generators for the cohomology ring of the moduli space of rank 2 Higgs bundles, Proc. London Math. Soc. (3), 632-658 (2004) ·Zbl 1060.14048 ·doi:10.1112/S0024611503014618 |
| [26] | Huybrechts, Daniel, The geometry of moduli spaces of sheaves, Aspects of Mathematics, E31, xiv+269 pp. (1997), Friedr. Vieweg & Sohn, Braunschweig ·Zbl 0872.14002 ·doi:10.1007/978-3-663-11624-0 |
| [27] | Hitchin, Nigel, Stable bundles and integrable systems, Duke Math. J., 91-114 (1987) ·Zbl 0627.14024 ·doi:10.1215/S0012-7094-87-05408-1 |
| [28] | Le Potier, J., Faisceaux semi-stables de dimension \(1\) sur le plan projectif, Rev. Roumaine Math. Pures Appl., 635-678 (1993) ·Zbl 0815.14029 |
| [29] | Le Potier, Joseph, Syst\`emes coh\'{e}rents et structures de niveau, Ast\'{e}risque, 143 pp. (1993) ·Zbl 0881.14008 |
| [30] | Markman, Eyal, Generators of the cohomology ring of moduli spaces of sheaves on symplectic surfaces, J. Reine Angew. Math., 61-82 (2002) ·Zbl 0988.14019 ·doi:10.1515/crll.2002.028 |
| [31] | Markman, Eyal, Integral generators for the cohomology ring of moduli spaces of sheaves over Poisson surfaces, Adv. Math., 622-646 (2007) ·Zbl 1115.14036 ·doi:10.1016/j.aim.2006.03.006 |
| [32] | Markman, Eyal, On the monodromy of moduli spaces of sheaves on \(K3\) surfaces, J. Algebraic Geom., 29-99 (2008) ·Zbl 1185.14015 ·doi:10.1090/S1056-3911-07-00457-2 |
| [33] | Markman, Eyal, Algebraic and complex geometry. Lagrangian fibrations of holomorphic-symplectic varieties of \(K3^{[n]}\)-type, Springer Proc. Math. Stat., 241-283 (2014), Springer, Cham ·Zbl 1319.53102 ·doi:10.1007/978-3-319-05404-9\_10 |
| [34] | E. Markman, The monodromy of generalized Kummer varieties and algebraic cycles on their intermediate Jacobians, 1805.11574, 2018. |
| [35] | Maulik, Davesh, Gopakumar-Vafa invariants via vanishing cycles, Invent. Math., 1017-1097 (2018) ·Zbl 1400.14141 ·doi:10.1007/s00222-018-0800-6 |
| [36] | A. Mellit, Cell decompositions of character varieties, 1905.10685, 2019. |
| [37] | Mumford, David, Geometric invariant theory, Ergebnisse der Mathematik und ihrer Grenzgebiete, (N.F.), Band 34, vi+145 pp. (1965), Springer-Verlag, Berlin-New York ·Zbl 0147.39304 |
| [38] | J. Shen and Q. Yin, Topology of Lagrangian fibrations and Hodge theory and Hodge theory of hyper-K\"ahler manifolds, Appendix by Claire Voisin, Duke Math. J., to appear. |
| [39] | J. Shen and Z. Zhang, Perverse filtrations, Hilbert schemes, and the P=W conjecture for parabolic Higgs bundles, Algebr. Geom., 8 (4), 2021, pp. 465-489. ·Zbl 1483.14033 |
| [40] | Shende, Vivek, The weights of the tautological classes of character varieties, Int. Math. Res. Not. IMRN, 6832-6840 (2017) ·Zbl 1405.14037 ·doi:10.1093/imrn/rnv363 |
| [41] | Simpson, Carlos T., Higgs bundles and local systems, Inst. Hautes \'{E}tudes Sci. Publ. Math., 5-95 (1992) ·Zbl 0814.32003 |
| [42] | Simpson, Carlos T., Moduli of representations of the fundamental group of a smooth projective variety. II, Inst. Hautes \'{E}tudes Sci. Publ. Math., 5-79 (1995) (1994) ·Zbl 0891.14006 |
| [43] | Williamson, Geordie, The Hodge theory of the decomposition theorem, Ast\'{e}risque, Exp. No. 1115, 335-367 (2017) ·Zbl 1373.14010 |
| [44] | Yoshioka, K\={o}ta, Moduli spaces of stable sheaves on abelian surfaces, Math. Ann., 817-884 (2001) ·Zbl 1066.14013 ·doi:10.1007/s002080100255 |
| [45] | Zhang, Zili, Multiplicativity of perverse filtration for Hilbert schemes of fibered surfaces, Adv. Math., 636-679 (2017) ·Zbl 1401.14190 ·doi:10.1016/j.aim.2017.03.028 |
