Geometry & Topology Volume 22, issue 6 (2018)

Download this article
	For screen
	For printing

Recent Issues

The Journal

Submission Guidelines

Submission Page

Policies for Authors

Ethics Statement

ISSN 1364-0380 (online)

ISSN 1465-3060 (print)

Author Index

To Appear

Other MSP Journals

Faithful actions from hyperplane arrangements

Yuki Hirano and Michael Wemyss

Geometry & Topology 22 (2018) 3395–3433

DOI: 10.2140/gt.2018.22.3395

Bibliography

1	M Van den Bergh, Three-dimensional flops and noncommutative rings, Duke Math. J. 122 (2004) 423 MR2057015
2	A Bondal, D Orlov, Reconstruction of a variety from the derived category and groups of autoequivalences, Compositio Math. 125 (2001) 327 MR1818984
3	C Brav, H Thomas, Braid groups and Kleinian singularities, Math. Ann. 351 (2011) 1005 MR2854121
4	S Brenner, M C R Butler, A spectral sequence analysis of classical tilting functors, from: "Handbook of tilting theory" (editors L Angeleri Hügel, D Happel, H Krause), London Math. Soc. Lecture Note Ser. 332, Cambridge Univ. Press (2007) 31 MR2384607
5	H Cartan, S Eilenberg, Homological algebra, Princeton Univ. Press (1956)
6	I Cheltsov, C Shramov, Cremona groups and the icosahedron, CRC (2016) MR3444095
7	P Deligne, Les immeubles des groupes de tresses généralisés, Invent. Math. 17 (1972) 273 MR0422673
8	L Demonet, O Iyama, G Jasso, τ–tilting finite algebras, bricks and g–vectors, Int. Math. Res. Not. (2017)
9	P Deshpande, Arrangements of submanifolds and the tangent bundle complement, PhD thesis, The University of Western Ontario (2011)
10	W Donovan, M Wemyss, Twists and braids for general 3–fold flops, preprint (2015) arXiv:1504.05320
11	W Donovan, M Wemyss, Noncommutative deformations and flops, Duke Math. J. 165 (2016) 1397 MR3504176
12	D Happel, I Reiten, S O Smalø, Tilting in abelian categories and quasitilted algebras, 575, Amer. Math. Soc. (1996) MR1327209
13	D Happel, L Unger, On a partial order of tilting modules, Algebr. Represent. Theory 8 (2005) 147 MR2162278
14	L Hille, On the volume of a tilting module, Abh. Math. Sem. Univ. Hamburg 76 (2006) 261 MR2293445
15	O Iyama, I Reiten, Fomin–Zelevinsky mutation and tilting modules over Calabi–Yau algebras, Amer. J. Math. 130 (2008) 1087 MR2427009
16	O Iyama, M Wemyss, Affine actions on 3–folds via contracted preprojective algebras and Tits cone intersections, in preparation
17	O Iyama, M Wemyss, Maximal modifications and Auslander–Reiten duality for non-isolated singularities, Invent. Math. 197 (2014) 521 MR3251829
18	O Iyama, M Wemyss, Reduction of triangulated categories and maximal modification algebras for cA_n singularities, J. Reine Angew. Math. (2015)
19	S Katz, Small resolutions of Gorenstein threefold singularities, from: "Algebraic geometry" (editors B Harbourne, R Speiser), Contemp. Math. 116, Amer. Math. Soc. (1991) 61 MR1108632
20	L Paris, The covers of a complexified real arrangement of hyperplanes and their fundamental groups, Topology Appl. 53 (1993) 75 MR1243871
21	L Paris, Universal cover of Salvetti’s complex and topology of simplicial arrangements of hyperplanes, Trans. Amer. Math. Soc. 340 (1993) 149 MR1148044
22	L Paris, On the fundamental group of the complement of a complex hyperplane arrangement, from: "Arrangements" (editors M Falk, H Terao), Adv. Stud. Pure Math. 27, Kinokuniya (2000) 257 MR1796904
23	H C Pinkham, Factorization of birational maps in dimension 3, from: "Singularities, II" (editor P Orlik), Proc. Sympos. Pure Math. 40, Amer. Math. Soc. (1983) 343 MR713260
24	C Riedtmann, A Schofield, On a simplicial complex associated with tilting modules, Comment. Math. Helv. 66 (1991) 70 MR1090165
25	M Salvetti, Topology of the complement of real hyperplanes in C^N, Invent. Math. 88 (1987) 603 MR884802
26	P Seidel, R Thomas, Braid group actions on derived categories of coherent sheaves, Duke Math. J. 108 (2001) 37 MR1831820
27	Y Sekiya, K Yamaura, Tilting theoretical approach to moduli spaces over preprojective algebras, Algebr. Represent. Theory 16 (2013) 1733 MR3127356
28	R G Swan, Induced representations and projective modules, Ann. of Math. 71 (1960) 552 MR0138688
29	M Wemyss, Flops and clusters in the homological minimal model programme, Invent. Math. 211 (2018) 435 MR3748312