Recent Issues
Volume 28, 3 issues
Volume 28
Issue 3, 1005–1499
Issue 2, 497–1003
Issue 1, 1–496
Volume 27, 9 issues
Volume 27
Issue 9, 3387–3831
Issue 8, 2937–3385
Issue 7, 2497–2936
Issue 6, 2049–2496
Issue 5, 1657–2048
Issue 4, 1273–1655
Issue 3, 823–1272
Issue 2, 417–821
Issue 1, 1–415
Volume 26, 8 issues
Volume 26
Issue 8, 3307–3833
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 25
Issue 7, 3257–3753
Issue 6, 2713–3256
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 24
Issue 7, 3219–3748
Issue 6, 2675–3218
Issue 5, 2149–2674
Issue 4, 1615–2148
Issue 3, 1075–1614
Issue 2, 533–1073
Issue 1, 1–532
Volume 23, 7 issues
Volume 23
Issue 7, 3233–3749
Issue 6, 2701–3231
Issue 5, 2165–2700
Issue 4, 1621–2164
Issue 3, 1085–1619
Issue 2, 541–1084
Issue 1, 1–540
Volume 22, 7 issues
Volume 22
Issue 7, 3761–4380
Issue 6, 3145–3760
Issue 5, 2511–3144
Issue 4, 1893–2510
Issue 3, 1267–1891
Issue 2, 645–1266
Issue 1, 1–644
Volume 21, 6 issues
Volume 21
Issue 6, 3191–3810
Issue 5, 2557–3190
Issue 4, 1931–2555
Issue 3, 1285–1930
Issue 2, 647–1283
Issue 1, 1–645
Volume 20, 6 issues
Volume 20
Issue 6, 3057–3673
Issue 5, 2439–3056
Issue 4, 1807–2438
Issue 3, 1257–1806
Issue 2, 629–1255
Issue 1, 1–627
Volume 19, 6 issues
Volume 19
Issue 6, 3031–3656
Issue 5, 2407–3030
Issue 4, 1777–2406
Issue 3, 1155–1775
Issue 2, 525–1154
Issue 1, 1–523
Volume 18, 5 issues
Volume 18
Issue 5, 2487–3110
Issue 4, 1865–2486
Issue 3, 1245–1863
Issue 2, 617–1244
Issue 1, 1–616
Volume 17, 5 issues
Volume 17
Issue 5, 2513–3134
Issue 4, 1877–2512
Issue 3, 1253–1876
Issue 2, 621–1252
Issue 1, 1–620
Volume 16, 4 issues
Volume 16
Issue 4, 1881–2516
Issue 3, 1247–1880
Issue 2, 625–1246
Issue 1, 1–624
Volume 15, 4 issues
Volume 15
Issue 4, 1843–2457
Issue 3, 1225–1842
Issue 2, 609–1224
Issue 1, 1–607
Volume 14, 5 issues
Volume 14
Issue 5, 2497–3000
Issue 4, 1871–2496
Issue 3, 1243–1870
Issue 2, 627–1242
Issue 1, 1–626
Volume 13, 5 issues
Volume 13
Issue 5, 2427–3054
Issue 4, 1835–2425
Issue 3, 1229–1833
Issue 2, 623–1227
Issue 1, 1–621
Volume 12, 5 issues
Volume 12
Issue 5, 2517–2855
Issue 4, 1883–2515
Issue 3, 1265–1882
Issue 2, 639–1263
Issue 1, 1–637
Volume 11, 4 issues
Volume 11
Issue 4, 1855–2440
Issue 3, 1255–1854
Issue 2, 643–1254
Issue 1, 1–642
Volume 10, 4 issues
Volume 10
Issue 4, 1855–2504
Issue 3, 1239–1853
Issue 2, 619–1238
Issue 1, 1–617
Volume 9, 4 issues
Volume 9
Issue 4, 1775–2415
Issue 3, 1187–1774
Issue 2, 571–1185
Issue 1, 1–569
Volume 8, 3 issues
Volume 8
Issue 3, 1013–1499
Issue 2, 511–1012
Issue 1, 1–509
Volume 7, 2 issues
Volume 7
Issue 2, 569–1073
Issue 1, 1–568
Volume 6, 2 issues
Volume 6
Issue 2, 495–990
Issue 1, 1–494
Volume 5, 2 issues
Volume 5
Issue 2, 441–945
Issue 1, 1–440
Volume 4, 1 issue
Volume 3, 1 issue
Volume 2, 1 issue
Volume 1, 1 issue
1
H Abban , Z
Zhuang , K–stability of Fano
varieties via admissible flags , Forum Math. Pi 10
(2022) MR4448177
2
K Altmann , J
Hausen , Polyhedral divisors
and algebraic torus actions , Math. Ann. 334 (2006) 557
MR2207875
3
K Altmann , J
Hausen , H Süss , Gluing affine torus
actions via divisorial fans , Transform. Groups 13
(2008) 215 MR2426131
4
R Bamler , Convergence of
Ricci flows with bounded scalar curvature , Ann. of
Math. 188 (2018) 753 MR3866886
5
R J Berman ,
K–polystability of
ℚ –Fano varieties admitting
Kähler–Einstein metrics , Invent. Math. 203 (2016) 973
MR3461370
6
R J Berman , S
Boucksom , P Eyssidieux , V Guedj , A
Zeriahi , Kähler–Einstein
metrics and the Kähler–Ricci flow on log Fano
varieties , J. Reine Angew. Math. 751 (2019) 27 MR3956691
7
R J Berman , S
Boucksom , M Jonsson , A variational approach to
the Yau–Tian–Donaldson conjecture , J. Amer. Math. Soc.
34 (2021) 605 MR4334189
8
R J Berman ,
D W Nystrom , Complex optimal transport and the
pluripotential theory of Kähler–Ricci solitons , preprint
(2014) arXiv:1401.8264
9
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
10
H Blum , Existence of
valuations with smallest normalized volume , Compos.
Math. 154 (2018) 820 MR3778195
11
H Blum , M
Jonsson , Thresholds,
valuations, and K–stability , Adv. Math. 365 (2020)
107062 MR4067358
12
H Blum , Y Liu ,
The normalized
volume of a singularity is lower semicontinuous , J.
Eur. Math. Soc. 23 (2021) 1225 MR4228279
13
H Blum , Y Liu ,
Openness of
uniform K–stability in families of ℚ –Fano varieties , Ann. Sci. Éc. Norm.
Supér. 55 (2022) 1 MR4411858
14
H Blum , Y Liu ,
C Xu , Openness of
K–semistability for Fano varieties , Duke Math. J. 171
(2022) 2753 MR4505846
15
H Blum , Y Liu ,
C Xu , Z Zhuang , The existence of the
Kähler–Ricci soliton degeneration , Forum Math. Pi 11
(2023) MR4558985
16
H Blum , Y Liu ,
C Zhou , Optimal
destabilization of K–unstable Fano varieties via stability
thresholds , Geom. Topol. 26 (2022) 2507 MR4521248
17
S Boucksom , H
Chen , Okounkov bodies of
filtered linear series , Compos. Math. 147 (2011) 1205
MR2822867
18
S Boucksom , D
Eriksson , Spaces of norms,
determinant of cohomology and Fekete points in non-Archimedean
geometry , Adv. Math. 378 (2021) 107501 MR4192993
19
S Boucksom , T
Hisamoto , M Jonsson , Uniform K–stability,
Duistermaat–Heckman measures and singularities of
pairs , Ann. Inst. Fourier (Grenoble) 67 (2017) 743
MR3669511
20
S Boucksom , M
Jonsson , A non-Archimedean approach to K–stability ,
preprint (2018) arXiv:1805.11160v1
21
S Boucksom , M
Jonsson , A non-Archimedean approach to K–stability, I :
Metric geometry of spaces of test configurations and
valuations , preprint (2021) arXiv:2107.11221
22
S Boucksom , A
Küronya , C Maclean , T Szemberg , Vanishing sequences
and Okounkov bodies , Math. Ann. 361 (2015) 811 MR3319549
23
M Brion , Sur l’image de
l’application moment , from: "Séminaire d’algèbre Paul
Dubreil et Marie-Paule Malliavin" (editor M P Malliavin),
Lecture Notes in Math. 1296, Springer (1987) 177 MR0932055
24
H Chen , C
Maclean , Distribution of
logarithmic spectra of the equilibrium energy ,
Manuscripta Math. 146 (2015) 365 MR3312451
25
X Chen , S
Donaldson , S Sun , Kähler–Einstein
metrics on Fano manifolds, I : Approximation of metrics with
cone singularities , J. Amer. Math. Soc. 28 (2015) 183
MR3264766
26
X Chen , S
Donaldson , S Sun , Kähler–Einstein
metrics on Fano manifolds, II : Limits with cone angle less
than 2 π , J. Amer. Math. Soc. 28 (2015) 199
MR3264767
27
X Chen , S
Donaldson , S Sun , Kähler–Einstein
metrics on Fano manifolds, III : Limits as cone angle
approaches 2 π and completion of the main proof , J.
Amer. Math. Soc. 28 (2015) 235 MR3264768
28
X Chen , S Sun ,
B Wang , Kähler–Ricci flow,
Kähler–Einstein metric, and K–stability , Geom. Topol.
22 (2018) 3145 MR3858762
29
X Chen , B Wang ,
Space of
Ricci flows, II : Part B : weak compactness of the
flows , J. Differential Geom. 116 (2020) 1 MR4146357
30
T Darvas , W He ,
Geodesic rays
and Kähler–Ricci trajectories on Fano manifolds , Trans.
Amer. Math. Soc. 369 (2017) 5069 MR3632560
31
R Dervan , G
Székelyhidi , The Kähler–Ricci flow
and optimal degenerations , J. Differential Geom. 116
(2020) 187 MR4146359
32
S K Donaldson ,
Scalar
curvature and stability of toric varieties , J.
Differential Geom. 62 (2002) 289 MR1988506
33
S K Donaldson ,
Lower bounds
on the Calabi functional , J. Differential Geom. 70
(2005) 453 MR2192937
34
S Donaldson , S
Sun , Gromov–Hausdorff
limits of Kähler manifolds and algebraic geometry, II ,
J. Differential Geom. 107 (2017) 327 MR3707646
35
L Ein , R
Lazarsfeld , K E Smith , Uniform approximation
of Abhyankar valuation ideals in smooth function
fields , Amer. J. Math. 125 (2003) 409 MR1963690
36
K Fujita , Optimal bounds for the
volumes of Kähler–Einstein Fano manifolds , Amer. J.
Math. 140 (2018) 391 MR3783213
37
K Fujita , A valuative
criterion for uniform K–stability of ℚ –Fano varieties , J. Reine Angew.
Math. 751 (2019) 309 MR3956698
38
K Fujita , Y
Odaka , On the K–stability of
Fano varieties and anticanonical divisors , Tohoku Math.
J. 70 (2018) 511 MR3896135
39
J Han , C Li ,
On the
Yau–Tian–Donaldson conjecture for generalized Kähler–Ricci
soliton equations , Comm. Pure Appl. Math. 76 (2023)
1793 MR4612573
40
W He , Kähler–Ricci
soliton and H –functional ,
Asian J. Math. 20 (2016) 645 MR3570456
41
T Hisamoto ,
Stability and coercivity for toric polarizations ,
preprint (2016) arXiv:1610.07998
42
T Hisamoto ,
Mabuchi’s soliton metric and relative D–stability ,
preprint (2019) arXiv:1905.05948
43
T Hisamoto ,
Geometric
flow, multiplier ideal sheaves and optimal destabilizer for a
Fano manifold , J. Geom. Anal. 33 (2023) 265 MR4602002
44
M Jonsson , M
Mustaţă , Valuations and asymptotic
invariants for sequences of ideals , Ann. Inst. Fourier
(Grenoble) 62 (2012) 2145 MR3060755
45
K Kaveh , A G
Khovanskii , Newton–Okounkov
bodies, semigroups of integral points, graded algebras and
intersection theory , Ann. of Math. 176 (2012) 925
MR2950767
46
K Kaveh , A
Khovanskii , Convex bodies and
multiplicities of ideals , Proc. Steklov Inst. Math. 286
(2014) 268 MR3482603
47
S J Kovács , Z
Patakfalvi , Projectivity of the moduli
space of stable log-varieties and subadditivity of log-Kodaira
dimension , J. Amer. Math. Soc. 30 (2017) 959 MR3671934
48
R Lazarsfeld ,
Positivity in
algebraic geometry, II : Positivity for vector bundles, and
multiplier ideals , 49, Springer (2004) MR2095472
49
R Lazarsfeld , M
Mustaţă , Convex bodies associated
to linear series , Ann. Sci. Éc. Norm. Supér. 42 (2009)
783 MR2571958
50
C Li , K-semistability is
equivariant volume minimization , Duke Math. J. 166
(2017) 3147 MR3715806
51
C Li , Minimizing
normalized volumes of valuations , Math. Z. 289 (2018)
491 MR3803800
52
C Li , G –uniform stability and Kähler–Einstein
metrics on Fano varieties , Invent. Math. 227 (2022) 661
MR4372222
53
C Li , Y Liu ,
Kähler–Einstein
metrics and volume minimization , Adv. Math. 341 (2019)
440 MR3872852
54
C Li , Y Liu ,
C Xu , A guided tour to
normalized volume , from: "Geometric analysis : in honor
of Gang Tian’s 60th birthday" (editors J Chen, P Lu, Z Lu, Z
Zhang), Progr. Math. 333, Springer (2020) 167 MR4181002
55
C Li , X Wang ,
C Xu , Algebraicity of the metric
tangent cones and equivariant K–stability , J. Amer.
Math. Soc. 34 (2021) 1175 MR4301561
56
C Li , C Xu ,
Special test
configuration and K–stability of Fano varieties , Ann.
of Math. 180 (2014) 197 MR3194814
57
C Li , C Xu ,
Stability of
valuations: higher rational rank , Peking Math. J. 1
(2018) 1 MR4059992
58
C Li , C Xu ,
Stability of
valuations and Kollár components , J. Eur. Math. Soc. 22
(2020) 2573 MR4118616
59
Y Li , Z Li ,
Equivariant ℝ –test
configurations and semistable limits of ℚ –Fano group compactifications , preprint
(2021) arXiv:2103.06439
60
Y Liu , The volume of
singular Kähler–Einstein Fano varieties , Compos. Math.
154 (2018) 1131 MR3797604
61
D Mumford ,
Stability of projective varieties , Enseign. Math. 23
(1977) 39 MR0450272
62
A Okounkov ,
Brunn–Minkowski
inequality for multiplicities , Invent. Math. 125 (1996)
405 MR1400312
63
W Rossmann ,
Equivariant multiplicities on complex varieties , from:
"Orbites unipotentes et représentations, III" (editor M
Andler), Astérisque 173–174, Soc. Math. France (1989) 313
MR1021516
64
G Székelyhidi ,
Filtrations and
test-configurations , Math. Ann. 362 (2015) 451 MR3343885
65
G Székelyhidi ,
The partial
C 0 –estimate along the continuity
method , J. Amer. Math. Soc. 29 (2016) 537 MR3454382
66
B Teissier ,
Valuations, deformations, and toric geometry , from:
"Valuation theory and its applications, II" (editors F V
Kuhlmann, S Kuhlmann, M Marshall), Fields Inst. Commun. 33,
Amer. Math. Soc. (2003) 361 MR2018565
67
G Tian , Kähler–Einstein metrics
with positive scalar curvature , Invent. Math. 130
(1997) 1 MR1471884
68
G Tian , K–stability and
Kähler–Einstein metrics , Comm. Pure Appl. Math. 68
(2015) 1085 MR3352459
69
G Tian , S
Zhang , Z Zhang , X Zhu , Perelman’s
entropy and Kähler–Ricci flow on a Fano manifold ,
Trans. Amer. Math. Soc. 365 (2013) 6669 MR3105766
70
G Tian , Z
Zhang , Regularity of
Kähler–Ricci flows on Fano manifolds , Acta Math. 216
(2016) 127 MR3508220
71
G Tian , X Zhu ,
A new
holomorphic invariant and uniqueness of Kähler–Ricci
solitons , Comment. Math. Helv. 77 (2002) 297 MR1915043
72
G Tian , X Zhu ,
Convergence of
Kähler–Ricci flow , J. Amer. Math. Soc. 20 (2007) 675
MR2291916
73
F Wang , X Zhu ,
Tian’s
partial C 0 –estimate implies Hamilton–Tian’s
conjecture , Adv. Math. 381 (2021) 107619 MR4206790
74
F Wang , X Zhu ,
Uniformly strong
convergence of Kähler–Ricci flows on a Fano manifold ,
Sci. China Math. 65 (2022) 2337 MR4499520
75
X J Wang , X
Zhu , Kähler–Ricci
solitons on toric manifolds with positive first Chern
class , Adv. Math. 188 (2004) 87 MR2084775
76
D Witt Nyström ,
Test
configurations and Okounkov bodies , Compos. Math. 148
(2012) 1736 MR2999302
77
M Xia , On sharp lower
bounds for Calabi-type functionals and destabilizing properties
of gradient flows , Anal. PDE 14 (2021) 1951 MR4308671
78
C Xu , A minimizing
valuation is quasi-monomial , Ann. of Math. 191 (2020)
1003 MR4088355
79
C Xu , Z Zhuang ,
On
positivity of the CM line bundle on K–moduli spaces ,
Ann. of Math. 192 (2020) 1005 MR4172625
80
C Xu , Z Zhuang ,
Uniqueness of the
minimizer of the normalized volume function , Camb. J.
Math. 9 (2021) 149 MR4325260
81
Y Yao , Relative Ding
stability and an obstruction to the existence of Mabuchi
solitons , J. Geom. Anal. 32 (2022) 105 MR4372898