Volume 25, issue 5 (2021)

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

Volume 26
Issue 7, 2855–3306
Issue 6, 2405–2853
Issue 5, 1907–2404
Issue 4, 1435–1905
Issue 3, 937–1434
Issue 2, 477–936
Issue 1, 1–476

Volume 25, 7 issues

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
Editorial Procedure
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
Moduli theory, stability of fibrations and optimal symplectic connections

Ruadhaí Dervan and Lars Martin Sektnan

Geometry & Topology 25 (2021) 2643–2697
Bibliography
1 R J Berman, K–polystability of –Fano varieties admitting Kähler–Einstein metrics, Invent. Math. 203 (2016) 973 MR3461370
2 B Berndtsson, Probability measures associated to geodesics in the space of Kähler metrics, from: "Algebraic and analytic microlocal analysis" (editors M Hitrik, D Tamarkin, B Tsygan, S Zelditch), Springer Proc. Math. Stat. 269, Springer (2018) 395 MR3903321
3 T Bouche, Convergence de la métrique de Fubini–Study d’un fibré linéaire positif, Ann. Inst. Fourier (Grenoble) 40 (1990) 117 MR1056777
4 S Boucksom, T Hisamoto, M Jonsson, Uniform K–stability, Duistermaat–Heckman measures and singularities of pairs, Ann. Inst. Fourier (Grenoble) 67 (2017) 743 MR3669511
5 G Codogni, Z Patakfalvi, Positivity of the CM line bundle for families of K-stable klt Fano varieties, Invent. Math. 223 (2021) 811 MR4213768
6 R Dervan, Uniform stability of twisted constant scalar curvature Kähler metrics, Int. Math. Res. Not. 2016 (2016) 4728 MR3564626
7 R Dervan, Relative K–stability for Kähler manifolds, Math. Ann. 372 (2018) 859 MR3880285
8 R Dervan, J Keller, A finite dimensional approach to Donaldson’s J–flow, Comm. Anal. Geom. 27 (2019) 1025 MR4037375
9 R Dervan, P Naumann, Moduli of polarised manifolds via canonical Kähler metrics, preprint (2018) arXiv:1810.02576
10 R Dervan, J Ross, Stable maps in higher dimensions, Math. Ann. 374 (2019) 1033 MR3985107
11 R Dervan, L M Sektnan, Optimal symplectic connections on holomorphic submersions, Comm. Pure Appl. Math. (2020)
12 S K Donaldson, Anti self-dual Yang–Mills connections over complex algebraic surfaces and stable vector bundles, Proc. Lond. Math. Soc. 50 (1985) 1 MR765366
13 S K Donaldson, Scalar curvature and projective embeddings, I, J. Differential Geom. 59 (2001) 479 MR1916953
14 S K Donaldson, Scalar curvature and stability of toric varieties, J. Differential Geom. 62 (2002) 289 MR1988506
15 S K Donaldson, Lower bounds on the Calabi functional, J. Differential Geom. 70 (2005) 453 MR2192937
16 D Eisenbud, J Harris, 3264 and all that : a second course in algebraic geometry, Cambridge Univ. Press (2016) MR3617981
17 J Fine, Fibrations with constant scalar curvature Kähler metrics and the CM–line bundle, Math. Res. Lett. 14 (2007) 239 MR2318622
18 J Fine, J Ross, A note on positivity of the CM–line bundle, Int. Math. Res. Not. 2006 (2006) MR2250009
19 A Fujiki, The moduli spaces and Kähler metrics of polarized algebraic varieties, Sugaku 42 (1990) 231 MR1073369
20 A Fujiki, G Schumacher, The moduli space of extremal compact Kähler manifolds and generalized Weil–Petersson metrics, Publ. Res. Inst. Math. Sci. 26 (1990) 101 MR1053910
21 W Fulton, Intersection theory, 2, Springer (1984) MR732620
22 R Hartshorne, Algebraic geometry, 52, Springer (1977) MR0463157
23 Y Hashimoto, Existence of twisted constant scalar curvature Kähler metrics with a large twist, Math. Z. 292 (2019) 791 MR3980270
24 S Kobayashi, Differential geometry of complex vector bundles, 15, Princeton Univ. Press (1987) MR909698
25 J Kollár, Rational curves on algebraic varieties, 32, Springer (1996) MR1440180
26 M Lejmi, G Székelyhidi, The J–flow and stability, Adv. Math. 274 (2015) 404 MR3318155
27 C Li, X Wang, C Xu, Quasi-projectivity of the moduli space of smooth Kähler–Einstein Fano manifolds, Ann. Sci. École Norm. Sup. 51 (2018) 739 MR3831036
28 C Li, X Wang, C Xu, On the proper moduli spaces of smoothable Kähler–Einstein Fano varieties, Duke Math. J. 168 (2019) 1387 MR3959862
29 C Li, C Xu, Special test configuration and K–stability of Fano varieties, Ann. of Math. 180 (2014) 197 MR3194814
30 C Li, X Zhang, Q Zhao, A note on the generalization of the Kodaira embedding theorem, Sci. China Math. 64 (2021) 1563 MR4280368
31 H Luo, Geometric criterion for Gieseker–Mumford stability of polarized manifolds, J. Differential Geom. 49 (1998) 577 MR1669716
32 A Moriwaki, The continuity of Deligne’s pairing, Int. Math. Res. Not. 1999 (1999) 1057 MR1725483
33 D Mumford, Geometric invariant theory, 34, Springer (1965) MR0214602
34 Y Odaka, On the moduli of Kähler–Einstein Fano manifolds, preprint (2012) arXiv:1211.4833
35 Y Odaka, A generalization of the Ross–Thomas slope theory, Osaka J. Math. 50 (2013) 171 MR3080636
36 Y Odaka, Compact moduli spaces of Kähler–Einstein Fano varieties, Publ. Res. Inst. Math. Sci. 51 (2015) 549 MR3395458
37 J Ross, R Thomas, An obstruction to the existence of constant scalar curvature Kähler metrics, J. Differential Geom. 72 (2006) 429 MR2219940
38 J Ross, R Thomas, A study of the Hilbert–Mumford criterion for the stability of projective varieties, J. Algebraic Geom. 16 (2007) 201 MR2274514
39 J Ross, R Thomas, Weighted projective embeddings, stability of orbifolds, and constant scalar curvature Kähler metrics, J. Differential Geom. 88 (2011) 109 MR2819757
40 C T Simpson, Moduli of representations of the fundamental group of a smooth projective variety, I, Inst. Hautes Études Sci. Publ. Math. 79 (1994) 47 MR1307297
41 J Stoppa, E Tenni, A simple limit for slope instability, Int. Math. Res. Not. 2010 (2010) 1816 MR2646342
42 G Székelyhidi, An introduction to extremal Kähler metrics, 152, Amer. Math. Soc. (2014) MR3186384
43 G Székelyhidi, Filtrations and test-configurations, Math. Ann. 362 (2015) 451 MR3343885
44 R P Thomas, Notes on GIT and symplectic reduction for bundles and varieties, from: "Surveys in differential geometry, X" (editor S T Yau), International (2006) 221 MR2408226
45 G Tian, On a set of polarized Kähler metrics on algebraic manifolds, J. Differential Geom. 32 (1990) 99 MR1064867
46 G Tian, Kähler–Einstein metrics with positive scalar curvature, Invent. Math. 130 (1997) 1 MR1471884
47 K Uhlenbeck, S T Yau, On the existence of Hermitian–Yang–Mills connections in stable vector bundles, Comm. Pure Appl. Math. 39 (1986) MR861491
48 X Wang, Balance point and stability of vector bundles over a projective manifold, Math. Res. Lett. 9 (2002) 393 MR1909652
49 X Wang, Moment map, Futaki invariant and stability of projective manifolds, Comm. Anal. Geom. 12 (2004) 1009 MR2103309
50 X Wang, Canonical metrics on stable vector bundles, Comm. Anal. Geom. 13 (2005) 253 MR2154820
51 X Wang, Height and GIT weight, Math. Res. Lett. 19 (2012) 909 MR3008424
52 X Wang, C Xu, Nonexistence of asymptotic GIT compactification, Duke Math. J. 163 (2014) 2217 MR3263033
53 D Witt Nyström, Test configurations and Okounkov bodies, Compos. Math. 148 (2012) 1736 MR2999302
54 S T Yau, Open problems in geometry, from: "Differential geometry: partial differential equations on manifolds" (editor R Greene), Proc. Sympos. Pure Math. 54, Amer. Math. Soc. (1993) 1 MR1216573
55 Y Zeng, Deformations from a given Kähler metric to a twisted cscK metric, Asian J. Math. 23 (2019) 985 MR4136486
56 S Zhang, Heights and reductions of semi-stable varieties, Compos. Math. 104 (1996) 77 MR1420712