Geometry & Topology Volume 27, issue 1 (2023)

Download this article
	For screen
	For printing

Recent Issues

The Journal

Submission Guidelines

Submission Page

Policies for Authors

Ethics Statement

ISSN (electronic): 1364-0380

ISSN (print): 1465-3060

Author Index

To Appear

Other MSP Journals

Symplectic resolutions of character varieties

Gwyn Bellamy and Travis Schedler

Geometry & Topology 27 (2023) 51–86

DOI: 10.2140/gt.2023.27.51

Bibliography

1	A Aizenbud, N Avni, Representation growth and rational singularities of the moduli space of local systems, Invent. Math. 204 (2016) 245 MR3480557
2	A Alekseev, A Malkin, E Meinrenken, Lie group valued moment maps, J. Differential Geom. 48 (1998) 445 MR1638045
3	M Artin, On the solutions of analytic equations, Invent. Math. 5 (1968) 277 MR232018
4	M Artin, Algebraic approximation of structures over complete local rings, Inst. Hautes Études Sci. Publ. Math. 36 (1969) 23 MR268188
5	A Beauville, Variétés Kähleriennes dont la première classe de Chern est nulle, J. Differential Geom. 18 (1983) 755 MR730926
6	A Beauville, Symplectic singularities, Invent. Math. 139 (2000) 541 MR1738060
7	G Bellamy, T Schedler, On the (non)existence of symplectic resolutions of linear quotients, Math. Res. Lett. 23 (2016) 1537 MR3621098
8	G Bellamy, T Schedler, On symplectic resolutions and factoriality of Hamiltonian reductions, Math. Ann. 375 (2019) 165 MR4000238
9	G Bellamy, T Schedler, Symplectic resolutions of quiver varieties, Selecta Math. 27 (2021) MR4265941
10	M Van den Bergh, Double Poisson algebras, Trans. Amer. Math. Soc. 360 (2008) 5711 MR2425689
11	C Birkar, P Cascini, C D Hacon, J McKernan, Existence of minimal models for varieties of log general type, J. Amer. Math. Soc. 23 (2010) 405 MR2601039
12	R Bocklandt, F Galluzzi, F Vaccarino, The Nori–Hilbert scheme is not smooth for 2–Calabi–Yau algebras, J. Noncommut. Geom. 10 (2016) 745 MR3519051
13	S Boissière, O Gabber, O Serman, Sur le produit de variétés localement factorielles ou ℚ–factorielles, preprint (2014) arXiv:1104.1861v3
14	J F Boutot, Singularités rationnelles et quotients par les groupes réductifs, Invent. Math. 88 (1987) 65 MR877006
15	N Budur, Rational singularities, quiver moment maps, and representations of surface groups, Int. Math. Res. Not. 2021 (2021) 11782 MR4294133
16	N Budur, M Zordan, On representation zeta functions for special linear groups, Int. Math. Res. Not. 2020 (2020) 868 MR4073934
17	W Crawley-Boevey, Monodromy for systems of vector bundles and multiplicative preprojective algebras, Bull. Lond. Math. Soc. 45 (2013) 309 MR3064416
18	W Crawley-Boevey, P Shaw, Multiplicative preprojective algebras, middle convolution and the Deligne–Simpson problem, Adv. Math. 201 (2006) 180 MR2204754
19	J M Drezet, Points non factoriels des variétés de modules de faisceaux semi-stables sur une surface rationnelle, J. Reine Angew. Math. 413 (1991) 99 MR1089799
20	C Felisetti, M Mauri, P = W conjectures for character varieties with symplectic resolution, J. Éc. polytech. Math. 9 (2022) 853 MR4436035
21	H Flenner, Extendability of differential forms on nonisolated singularities, Invent. Math. 94 (1988) 317 MR958835
22	C Florentino, S Lawton, Singularities of free group character varieties, Pacific J. Math. 260 (2012) 149 MR3001789
23	B Fu, On ℚ–factorial terminalizations of nilpotent orbits, J. Math. Pures Appl. 93 (2010) 623 MR2651984
24	W L Gan, V Ginzburg, Almost-commuting variety, 𝒟–modules, and Cherednik algebras, Int. Math. Res. Pap. (2006) MR2210660
25	V Ginzburg, Lectures on Nakajima’s quiver varieties, from: "Geometric methods in representation theory, I" (editor M Brion), Sémin. Congr. 24, Soc. Math. France (2012) 145 MR3202703
26	W M Goldman, The symplectic nature of fundamental groups of surfaces, Adv. in Math. 54 (1984) 200 MR762512
27	W M Goldman, Invariant functions on Lie groups and Hamiltonian flows of surface group representations, Invent. Math. 85 (1986) 263 MR846929
28	R Hermann, The formal linearization of a semisimple Lie algebra of vector fields about a singular point, Trans. Amer. Math. Soc. 130 (1968) 105 MR217225
29	A Joseph, On a Harish-Chandra homomorphism, C. R. Acad. Sci. Paris Sér. I Math. 324 (1997) 759 MR1446576
30	D Kaledin, Symplectic singularities from the Poisson point of view, J. Reine Angew. Math. 600 (2006) 135 MR2283801
31	D Kaledin, Geometry and topology of symplectic resolutions, from: "Algebraic geometry, II" (editors D Abramovich, A Bertram, L Katzarkov, R Pandharipande, M Thaddeus), Proc. Sympos. Pure Math. 80, Amer. Math. Soc. (2009) 595 MR2483948
32	D Kaledin, M Lehn, Local structure of hyperkähler singularities in O’Grady’s examples, Mosc. Math. J. 7 (2007) 653 MR2372208
33	D Kaledin, M Lehn, C Sorger, Singular symplectic moduli spaces, Invent. Math. 164 (2006) 591 MR2221132
34	D Kaplan, T Schedler, Multiplicative preprojective algebras are 2–Calabi–Yau, preprint (2021) arXiv:1905.12025v4
35	S Lawton, C Manon, Character varieties of free groups are Gorenstein but not always factorial, J. Algebra 456 (2016) 278 MR3484145
36	M Lehn, C Sorger, La singularité de O’Grady, J. Algebraic Geom. 15 (2006) 753 MR2237269
37	J Li, The space of surface group representations, Manuscripta Math. 78 (1993) 223 MR1206154
38	D Luna, Slices étales, from: "Sur les groupes algébriques", Mém. Soc. Math. France 33, Soc. Math. France (1973) 81 MR0342523
39	M Martino, Stratifications of Marsden–Weinstein reductions for representations of quivers and deformations of symplectic quotient singularities, Math. Z. 258 (2008) 1 MR2350030
40	J S Milne, Étale cohomology, 33, Princeton Univ. Press (1980) MR559531
41	Y Namikawa, A note on symplectic singularities, preprint (2001) arXiv:math/0101028
42	Y Namikawa, Poisson deformations of affine symplectic varieties, Duke Math. J. 156 (2011) 51 MR2746388
43	R W Richardson, Conjugacy classes of n–tuples in Lie algebras and algebraic groups, Duke Math. J. 57 (1988) 1 MR952224
44	T Schedler, A Tirelli, Symplectic resolutions for multiplicative quiver varieties and character varieties for punctured surfaces, from: "Representation theory and algebraic geometry" (editors V Baranovsky, N Guay, T Schedler), Birkhäuser (2022)
45	A S Sikora, Character varieties of abelian groups, Math. Z. 277 (2014) 241 MR3205770
46	A S Sikora, G–character varieties for G = SO(n, ℂ) and other not simply connected groups, J. Algebra 429 (2015) 324 MR3320627
47	C T Simpson, Moduli of representations of the fundamental group of a smooth projective variety, II, Inst. Hautes Études Sci. Publ. Math. 80 (1994) 5 MR1320603
48	A Tirelli, Symplectic resolutions for Higgs moduli spaces, Proc. Amer. Math. Soc. 147 (2019) 1399 MR3910407
49	J Wierzba, Contractions of symplectic varieties, J. Algebraic Geom. 12 (2003) 507 MR1966025