Geometry & Topology Volume 28, issue 7 (2024)

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

When does the zero fiber of the moment map have rational singularities?

Hans-Christian Herbig, Gerald W Schwarz and Christopher Seaton

Geometry & Topology 28 (2024) 3475–3510

DOI: 10.2140/gt.2024.28.3475

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 Aizenbud, N Avni, Counting points of schemes over finite rings and counting representations of arithmetic lattices, Duke Math. J. 167 (2018) 2721 MR3859363
3	M F Atiyah, R Bott, The Yang–Mills equations over Riemann surfaces, Philos. Trans. Roy. Soc. A 308 (1983) 523 MR0702806
4	L L Avramov, Complete intersections and symmetric algebras, J. Algebra 73 (1981) 248 MR0641643
5	A Beauville, Symplectic singularities, Invent. Math. 139 (2000) 541 MR1738060
6	D Birkes, Orbits of linear algebraic groups, Ann. of Math. 93 (1971) 459 MR0296077
7	S Boissière, O Gabber, O Serman, Sur le produit de variétés localement factorielles ou ℚ–factorielles, preprint (2011) arXiv:1104.1861
8	A Borel, Linear algebraic groups, 126, Springer (1991) MR1102012
9	J F Boutot, Singularités rationnelles et quotients par les groupes réductifs, Invent. Math. 88 (1987) 65 MR0877006
10	N Budur, Rational singularities, quiver moment maps, and representations of surface groups, Int. Math. Res. Not. 2021 (2021) 11782 MR4294133
11	J Cape, H C Herbig, C Seaton, Symplectic reduction at zero angular momentum, J. Geom. Mech. 8 (2016) 13 MR3485920
12	J Draisma, H Kraft, J Kuttler, Nilpotent subspaces of maximal dimension in semi-simple Lie algebras, Compos. Math. 142 (2006) 464 MR2218906
13	J M Drézet, Luna’s slice theorem and applications, from: "Algebraic group actions and quotients" (editor J A Wiśniewski), Hindawi (2004) 39 MR2210794
14	B Fu, Symplectic resolutions for nilpotent orbits, Invent. Math. 151 (2003) 167 MR1943745
15	M Gerstenhaber, On nilalgebras and linear varieties of nilpotent matrices, I, Amer. J. Math. 80 (1958) 614 MR0096678
16	I Glazer, Y I Hendel, On singularity properties of word maps and applications to probabilistic Waring type problems, 1497 (2024) arXiv:1912.12556 MR4790257
17	W M Goldman, The symplectic nature of fundamental groups of surfaces, Adv. Math. 54 (1984) 200 MR0762512
18	W M Goldman, Representations of fundamental groups of surfaces, from: "Geometry and topology" (editors J Alexander, J Harer), Lecture Notes in Math. 1167, Springer (1985) 95 MR0827264
19	R Hartshorne, Algebraic geometry, 52, Springer (1977) MR0463157
20	H C Herbig, G W Schwarz, The Koszul complex of a moment map, J. Symplectic Geom. 11 (2013) 497 MR3100804
21	H C Herbig, G W Schwarz, C Seaton, When is a symplectic quotient an orbifold?, Adv. Math. 280 (2015) 208 MR3350217
22	H C Herbig, G W Schwarz, C Seaton, Symplectic quotients have symplectic singularities, Compos. Math. 156 (2020) 613 MR4058942
23	H C Herbig, G W Schwarz, C Seaton, Isomorphisms of symplectic torus quotients, preprint (2023) arXiv:2306.17349
24	G Kapon, Singularity properties of graph varieties, preprint (2019) arXiv:1905.05847
25	F Knop, H Kraft, T Vust, The Picard group of a G–variety, from: "Algebraische Transformationsgruppen und Invariantentheorie" (editors H Kraft, P Slodowy, T A Springer), DMV Sem. 13, Birkhäuser (1989) 77 MR1044586
26	S J Kovács, A characterization of rational singularities, Duke Math. J. 102 (2000) 187 MR1749436
27	S Lawton, C Manon, Character varieties of free groups are Gorenstein but not always factorial, J. Algebra 456 (2016) 278 MR3484145
28	S Lawton, D Ramras, Covering spaces of character varieties, New York J. Math. 21 (2015) 383 MR3358550
29	S Lawton, A S Sikora, Varieties of characters, Algebr. Represent. Theory 20 (2017) 1133 MR3707908
30	J Li, The space of surface group representations, Manuscripta Math. 78 (1993) 223 MR1206154
31	D Luna, Slices étales, from: "Sur les groupes algébriques", Supp. Bull. Soc. Math. France 101, Soc. Math. France (1973) 81 MR0342523
32	D Luna, T Vust, Un théorème sur les orbites affines des groupes algébriques semi-simples, Ann. Scuola Norm. Sup. Pisa Cl. Sci. 27 (1973) 527 MR0364268
33	K J McGown, H R Parks, The generalization of Faulhaber’s formula to sums of non-integral powers, J. Math. Anal. Appl. 330 (2007) 571 MR2302942
34	R Meshulam, N Radwan, On linear subspaces of nilpotent elements in a Lie algebra, Linear Algebra Appl. 279 (1998) 195 MR1637881
35	M Mustaţă, Jet schemes of locally complete intersection canonical singularities, Invent. Math. 145 (2001) 397 MR1856396
36	Y Namikawa, Extension of 2–forms and symplectic varieties, J. Reine Angew. Math. 539 (2001) 123 MR1863856
37	D I Panyushev, The Jacobian modules of a representation of a Lie algebra and geometry of commuting varieties, Compos. Math. 94 (1994) 181 MR1302315
38	V L Popov, Criteria for the stability of the action of a semisimple group on the factorial of a manifold, Izv. Akad. Nauk SSSR Ser. Mat. 34 (1970) 523 MR0262416
39	R W Richardson, Conjugacy classes of n–tuples in Lie algebras and algebraic groups, Duke Math. J. 57 (1988) 1 MR0952224
40	G W Schwarz, Lifting smooth homotopies of orbit spaces, Inst. Hautes Études Sci. Publ. Math. 51 (1980) 37 MR0573821
41	G W Schwarz, Lifting differential operators from orbit spaces, Ann. Sci. École Norm. Sup. 28 (1995) 253 MR1326669
42	A Grothendieck, Cohomologie locale des faisceaux cohérents et théorèmes de Lefschetz locaux et globaux (SGA 2), 4, Soc. Math. France (2005) MR2171939
43	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