Volume 20, issue 3 (2016)

Download this article
Download this article For screen
For printing
Recent Issues

Volume 25
Issue 5, 2167–2711
Issue 4, 1631–2166
Issue 3, 1087–1630
Issue 2, 547–1085
Issue 1, 1–546

Volume 24, 7 issues

Volume 23, 7 issues

Volume 22, 7 issues

Volume 21, 6 issues

Volume 20, 6 issues

Volume 19, 6 issues

Volume 18, 5 issues

Volume 17, 5 issues

Volume 16, 4 issues

Volume 15, 4 issues

Volume 14, 5 issues

Volume 13, 5 issues

Volume 12, 5 issues

Volume 11, 4 issues

Volume 10, 4 issues

Volume 9, 4 issues

Volume 8, 3 issues

Volume 7, 2 issues

Volume 6, 2 issues

Volume 5, 2 issues

Volume 4, 1 issue

Volume 3, 1 issue

Volume 2, 1 issue

Volume 1, 1 issue

The Journal
About the Journal
Editorial Board
Editorial Interests
Subscriptions
 
Submission Guidelines
Submission Page
Policies for Authors
Ethics Statement
 
ISSN (electronic): 1364-0380
ISSN (print): 1465-3060
Author Index
To Appear
 
Other MSP Journals
Variation of Gieseker moduli spaces via quiver GIT

Daniel Greb, Julius Ross and Matei Toma

Geometry & Topology 20 (2016) 1539–1610
Bibliography
1 L Álvarez-Cónsul, Some results on the moduli spaces of quiver bundles, Geom. Dedicata 139 (2009) 99 MR2481840
2 L Álvarez-Cónsul, A King, A functorial construction of moduli of sheaves, Invent. Math. 168 (2007) 613 MR2299563
3 L Álvarez-Cónsul, A King, Moduli of sheaves from moduli of Kronecker modules, from: "Moduli spaces and vector bundles" (editors S B Bradlow, L Brambila-Paz, O García-Prada, S Ramanan), London Math. Soc. Lecture Note Ser. 359, Cambridge Univ. Press (2009) 212 MR2537070
4 I V Arzhantsev, J Hausen, Geometric invariant theory via Cox rings, J. Pure Appl. Algebra 213 (2009) 154 MR2462993
5 A Bertram, Some remarks on surface moduli and determinants, from: "Recent advances in algebraic geometry" (editors C D Hacon, M Mustaţă, M Popa), London Math. Soc. Lecture Note Ser. 417, Cambridge Univ. Press (2015) 13 MR3380441
6 N Bourbaki, Éléments de mathématique : Algèbre, Chapitres 1 à 3, Hermann (1970) MR0274237
7 C Chindris, Notes on GIT-fans for quivers, preprint (2008) arXiv:0805.1440v1
8 O Debarre, Higher-dimensional algebraic geometry, Springer (2001) MR1841091
9 I V Dolgachev, Y Hu, Variation of geometric invariant theory quotients, Inst. Hautes Études Sci. Publ. Math. (1998) 5 MR1659282
10 S K Donaldson, Irrationality and the h–cobordism conjecture, J. Differential Geom. 26 (1987) 141 MR892034
11 G Ellingsrud, L Göttsche, Variation of moduli spaces and Donaldson invariants under change of polarization, J. Reine Angew. Math. 467 (1995) 1 MR1355920
12 R Friedman, J W Morgan, On the diffeomorphism types of certain algebraic surfaces, I, J. Differential Geom. 27 (1988) 297 MR925124
13 R Friedman, Z Qin, Flips of moduli spaces and transition formulas for Donaldson polynomial invariants of rational surfaces, Comm. Anal. Geom. 3 (1995) 11 MR1362648
14 W Fulton, Intersection theory, 2, Springer (1998) MR1644323
15 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
16 L Göttsche, Change of polarization and Hodge numbers of moduli spaces of torsion free sheaves on surfaces, Math. Z. 223 (1996) 247 MR1417430
17 D Greb, Projectivity of analytic Hilbert and Kähler quotients, Trans. Amer. Math. Soc. 362 (2010) 3243 MR2592955
18 D Greb, J Ross, M Toma, Semi-continuity of stability for sheaves and variation of Gieseker moduli spaces, preprint (2015) arXiv:1501.04440v2
19 D Greb, M Toma, Compact moduli spaces for slope-semistable sheaves, preprint (2013) arXiv:1303.2480
20 A Grothendieck, Techniques de construction et théorèmes d’existence en géométrie algébrique, IV : Les schémas de Hilbert, from: "Séminaire Bourbaki 1960∕1961 (Exposè 221)", W A Benjamin (1966) MR1611822
21 M Halic, Quotients of affine spaces for actions of reductive groups, preprint (2004) arXiv:math/0412278v1
22 R Hartshorne, Algebraic geometry, 52, Springer (1977) MR0463157
23 P Heinzner, L Migliorini, Projectivity of moment map quotients, Osaka J. Math. 38 (2001) 167 MR1824905
24 Y Hu, W P Li, Variation of the Gieseker and Uhlenbeck compactifications, Internat. J. Math. 6 (1995) 397 MR1327156
25 D Huybrechts, M Lehn, The geometry of moduli spaces of sheaves, Cambridge Univ. Press (2010) MR2665168
26 D Joyce, Configurations in abelian categories, I : Basic properties and moduli stacks, Adv. Math. 203 (2006) 194 MR2231046
27 D Joyce, Configurations in abelian categories, II : Ringel–Hall algebras, Adv. Math. 210 (2007) 635 MR2303235
28 D Joyce, Configurations in abelian categories, III : Stability conditions and identities, Adv. Math. 215 (2007) 153 MR2354988
29 D Joyce, Configurations in abelian categories, IV : Invariants and changing stability conditions, Adv. Math. 217 (2008) 125 MR2357325
30 D Joyce, Y Song, A theory of generalized Donaldson–Thomas invariants, 1020, Amer. Math. Soc. (2012) MR2951762
31 Y H Kiem, J Li, A wall crossing formula of Donaldson–Thomas invariants without Chern–Simons functional, Asian J. Math. 17 (2013) 63 MR3038725
32 A D King, Moduli of representations of finite-dimensional algebras, Quart. J. Math. Oxford Ser. 45 (1994) 515 MR1315461
33 A Langer, Semistable sheaves in positive characteristic, Ann. of Math. 159 (2004) 251 MR2051393
34 S G Langton, Valuative criteria for families of vector bundles on algebraic varieties, Ann. of Math. 101 (1975) 88 MR0364255
35 A Laudin, A Schmitt, Recent results on quiver sheaves, Cent. Eur. J. Math. 10 (2012) 1246 MR2925600
36 J Le Potier, L’espace de modules de Simpson, exposé, SGA Jussieu (1992)
37 S Mac Lane, Categories for the working mathematician, 5, Springer (1998) MR1712872
38 K Matsuki, R Wentworth, Mumford–Thaddeus principle on the moduli space of vector bundles on an algebraic surface, Internat. J. Math. 8 (1997) 97 MR1433203
39 D Mumford, J Fogarty, F Kirwan, Geometric invariant theory, 34, Springer (1994) MR1304906
40 Z Qin, Equivalence classes of polarizations and moduli spaces of sheaves, J. Differential Geom. 37 (1993) 397 MR1205450
41 A Rudakov, Stability for an abelian category, J. Algebra 197 (1997) 231 MR1480783
42 A Schmitt, Walls for Gieseker semistability and the Mumford–Thaddeus principle for moduli spaces of sheaves over higher dimensional bases, Comment. Math. Helv. 75 (2000) 216 MR1774702
43 A Schmitt, Moduli for decorated tuples of sheaves and representation spaces for quivers, Proc. Indian Acad. Sci. Math. Sci. 115 (2005) 15 MR2120597
44 A H W Schmitt, Geometric invariant theory and decorated principal bundles, European Math. Soc. (2008) MR2437660
45 C T Simpson, Moduli of representations of the fundamental group of a smooth projective variety, I, Inst. Hautes Études Sci. Publ. Math. (1994) 47 MR1307297
46 A Teleman, Families of holomorphic bundles, Commun. Contemp. Math. 10 (2008) 523 MR2444847
47 M Thaddeus, Geometric invariant theory and flips, J. Amer. Math. Soc. 9 (1996) 691 MR1333296
48 K Yamada, A sequence of blowing-ups connecting moduli of sheaves and the Donaldson polynomial under change of polarization, J. Math. Kyoto Univ. 43 (2004) 829 MR2030801
49 K Yamada, Blowing-ups describing the polarization change of moduli schemes of semistable sheaves of general rank, Comm. Algebra 38 (2010) 3094 MR2730297