-
Notifications
You must be signed in to change notification settings - Fork 0
/
master doc.bbl
273 lines (213 loc) · 10.7 KB
/
master doc.bbl
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
256
257
258
259
260
261
262
263
264
265
266
267
268
269
270
271
272
273
\begin{thebibliography}{10}
\bibitem{poincare1908uniformisation}
H.~Poincar{\'e}, ``Sur l'uniformisation des fonctions analytiques,'' {\em Acta
mathematica}, vol.~31, no.~1, pp.~1--63, 1908.
\bibitem{koebe1909uniformisierung}
P.~Koebe, ``{\"U}ber die uniformisierung der algebraischen kurven. i,'' {\em
Mathematische Annalen}, vol.~67, no.~2, pp.~145--224, 1909.
\bibitem{koebe1910uniformisierung}
P.~Koebe, ``{\"U}ber die uniformisierung der algebraischen kurven. ii,'' {\em
Mathematische Annalen}, vol.~69, no.~1, pp.~1--81, 1910.
\bibitem{calabi54}
E.~Calabi, ``The space of {K}{\"a}hler metrics,'' {\em Proceedings of the
International Congress of Mathematicians}, vol.~2, pp.~206--207, 1956.
\bibitem{calabi57}
E.~Calabi, ``On {K}{\"a}hler manifolds with vanishing canonical class,'' {\em
Princeton Mathematical Series}, no.~12, pp.~78--89, 1957.
\bibitem{Aubin1976}
T.~Aubin, ``Equations du type {M}onge-{A}mp{\'e}re sur la varietes
{K}{\"a}hleriennes compactes,'' {\em CR Acad. Sci. Paris}, vol.~283,
pp.~119--121, 1976.
\bibitem{Yau1977}
S.-T. Yau, ``Calabi's conjecture and some new results in algebraic geometry,''
{\em Proceedings of the National Academy of Sciences}, vol.~74, no.~5,
pp.~1798--1799, 1977.
\bibitem{matsushima1957structure}
Y.~Matsushima, ``Sur la structure du groupe d'hom{\'e}omorphismes analytiques
d'une certaine vari{\'e}t{\'e} {K}aehl{\'e}rinne,'' {\em Nagoya Mathematical
Journal}, vol.~11, pp.~145--150, 1957.
\bibitem{futaki1983obstruction}
A.~Futaki, ``An obstruction to the existence of {E}instein {K}{\"a}hler
metrics,'' {\em Inventiones Mathematicae}, vol.~73, no.~3, pp.~437--443,
1983.
\bibitem{tian1987kahler}
G.~Tian, ``On {K}{\"a}hler-{E}instein metrics on certain {K}{\"a}hler manifolds
withc 1 (m)> 0,'' {\em Inventiones Mathematicae}, vol.~89, no.~2,
pp.~225--246, 1987.
\bibitem{chen2015kahler1}
X.~Chen, S.~Donaldson, and S.~Sun, ``{K}{\"a}hler-{E}instein metrics on {F}ano
manifolds. i: Approximation of metrics with cone singularities,'' {\em
Journal of the American Mathematical Society}, vol.~28, no.~1, pp.~183--197,
2015.
\bibitem{chen2015kahler2}
X.~Chen, S.~Donaldson, and S.~Sun, ``{K}{\"a}hler-{E}instein metrics on {F}ano
manifolds. ii: Limits with cone angle less than 2𝜋,'' {\em Journal of the
American Mathematical Society}, vol.~28, no.~1, pp.~199--234, 2015.
\bibitem{chen2015kahler3}
X.~Chen, S.~Donaldson, and S.~Sun, ``{K}{\"a}hler-{E}instein metrics on {F}ano
manifolds. iii: Limits as cone angle approaches 2𝜋 and completion of the
main proof,'' {\em Journal of the American Mathematical Society}, vol.~28,
no.~1, pp.~235--278, 2015.
\bibitem{datar2016kahler}
V.~Datar and G.~Sz{\'e}kelyhidi, ``{K}{\"a}hler--{E}instein metrics along the
smooth continuity method,'' {\em Geometric and Functional Analysis}, vol.~26,
no.~4, pp.~975--1010, 2016.
\bibitem{wang2004}
X.-J. Wang and X.~Zhu, ``{K}{\"a}hler--{R}icci solitons on toric manifolds with
positive first {C}hern class,'' {\em Advances in Mathematics}, vol.~188,
no.~1, pp.~87--103, 2004.
\bibitem{ilten2015}
N.~Ilten and H.~S{\"u}{\ss}, ``K-stability for {F}ano manifolds with torus
action of complexity 1,'' {\em Duke Math. J.}, vol.~166, no.~1, pp.~177--204,
2017.
\bibitem{suss2013kahler}
H.~S{\"u}{\ss}, ``{K}{\"a}hler--{E}instein metrics on symmetric {F}ano
$t$-varieties,'' {\em Advances in Mathematics}, vol.~246, pp.~100--113, 2013.
\bibitem{mori1981classification}
S.~Mori and S.~Mukai, ``Classification of {F}ano 3-folds with $b_2 \ge 2$,''
{\em Manuscripta Mathematica}, vol.~36, no.~2, pp.~147--162, 1981.
\bibitem{cable2019greatest}
J.~Cable, ``Greatest lower bounds on {R}icci curvature for {F}ano {T}-manifolds
of complexity one,'' {\em Bulletin of the London Mathematical Society},
vol.~51, no.~1, pp.~34--42, 2019.
\bibitem{li2009greatest}
C.~Li, ``Greatest lower bounds on {R}icci curvature for toric {F}ano
manifolds,'' {\em Advances in Mathematics}, vol.~226, pp.~4921--4932, 2011.
\bibitem{hausen2018torus}
J.~Hausen, C.~Hische, and M.~Wrobel, ``On torus actions of higher complexity,''
in {\em Forum of Mathematics, Sigma}, vol.~7, Cambridge University Press,
2019.
\bibitem{Su13}
H.~S{\"u}{\ss}, ``{K}{\"a}hler-{E}instein metrics on symmetric {{F}ano}
{$T$-varieties},'' {\em Advances in Mathematics}, vol.~246, pp.~100 -- 113,
2013.
\bibitem{griffiths}
P.~Griffiths and J.~Harris, ``Principles of algebraic geometry, pure and
applied mathematics,'' 1978.
\bibitem{chow1949compact}
W.-L. Chow, ``On compact complex analytic varieties,'' {\em American Journal of
Mathematics}, vol.~71, no.~4, pp.~893--914, 1949.
\bibitem{szebook}
G.~Sz{\'e}kelyhidi, {\em An introduction to extremal {K}{\"a}hler metrics},
vol.~152.
\newblock American Mathematical Soc., 2014.
\bibitem{yau1977calabi}
S.-T. Yau, ``Calabi's conjecture and some new results in algebraic geometry,''
{\em Proceedings of the National Academy of Sciences}, vol.~74, no.~5,
pp.~1798--1799, 1977.
\bibitem{yau1975}
S.-T. Yau, ``Harmonic functions on complete riemannian manifolds,'' {\em
Communications on Pure and Applied Mathematics}, vol.~28, no.~2,
pp.~201--228, 1975.
\bibitem{da2006symplectic}
A.~C. da~Silva, ``Symplectic geometry,'' in {\em Handbook of differential
geometry}, vol.~2, pp.~79--188, Elsevier, 2006.
\bibitem{berman2014complex}
R.~J. Berman and D.~W. Nystrom, ``Complex optimal transport and the
pluripotential theory of {K}{\"a}hler-{R}icci solitons,'' {\em ar{X}iv
preprint ar{X}iv:1401.8264}, 2014.
\bibitem{atiyah1982convexity}
M.~F. Atiyah, ``Convexity and commuting {H}amiltonians,'' {\em Bulletin of the
London Mathematical Society}, vol.~14, no.~1, pp.~1--15, 1982.
\bibitem{guillemin1982convexity}
V.~Guillemin and S.~Sternberg, ``Convexity properties of the moment mapping,''
{\em Inventiones Mathematicae}, vol.~67, no.~3, pp.~491--513, 1982.
\bibitem{cable2019general}
J.~Cable, ``{{K}{\"a}hler-{E}instein metrics on symmetric general arrangement
varieties}.'' 2019.
\bibitem{mumford1994}
D.~Mumford, J.~Fogarty, and F.~Kirwan, {\em Geometric invariant theory},
vol.~34.
\newblock Springer Science \& Business Media, 1994.
\bibitem{kempf1979}
G.~Kempf and L.~Ness, ``The length of vectors in representation spaces,'' in
{\em Algebraic geometry}, pp.~233--243, Springer, 1979.
\bibitem{kirwan}
F.~C. Kirwan, ``Partial desingularisations of quotients of nonsingular
varieties and their {B}etti numbers,'' {\em Annals of mathematics}, vol.~122,
no.~1, pp.~41--85, 1985.
\bibitem{kapranov1993}
M.~M. Kapranov, ``Chow quotients of {G}rassmannians. {I},'' {\em Adv. Soviet
Math}, vol.~16, no.~2, pp.~29--110, 1993.
\bibitem{baker2012}
H.~B{\"a}ker, J.~Hausen, and S.~Keicher, ``On {C}how quotients of torus
actions,'' {\em Michigan Math. J.}, vol.~64, no.~3, pp.~451--473, 2015.
\bibitem{altmann2006polyhedral}
K.~Altmann and J.~Hausen, ``Polyhedral divisors and algebraic torus actions,''
{\em Mathematische Annalen}, vol.~334, no.~3, pp.~557--607, 2006.
\bibitem{altmann2008gluing}
K.~Altmann, J.~Hausen, and H.~S{\"u}ss, ``Gluing affine torus actions via
divisorial fans,'' {\em Transformation Groups}, vol.~13, no.~2, pp.~215--242,
2008.
\bibitem{ilten2009polarized}
N.~O. Ilten and H.~S{\"u}{\ss}, ``Polarized complexity-1 {T}-varieties,'' {\em
Michigan Mathematical Journal}, vol.~60, pp.~561--578, 2011.
\bibitem{petersen2011torus}
L.~Petersen and H.~S{\"u}{\ss}, ``Torus invariant divisors,'' {\em Israel
Journal of Mathematics}, vol.~182, no.~1, pp.~481--504, 2011.
\bibitem{cable2018classification}
J.~Cable and H.~S{\"u}{\ss}, ``On the classification of {K}{\"a}hler--{R}icci
solitons on {G}orenstein del {P}ezzo surfaces,'' {\em European Journal of
Mathematics}, vol.~4, no.~1, pp.~137--161, 2018.
\bibitem{donaldson2008kahler}
S.~K. Donaldson, ``{K}{\"a}hler geometry on toric manifolds, and some other
manifolds with large symmetry,'' {\em Handbook of Geometric Analysis},
pp.~29--–75, 2008.
\bibitem{Barvinok1992}
Barvinok, ``Exponential sums and integrals overconvex polytopes,'' {\em Funct.
Anal. Appl.}, vol.~26(2):1, 1992.
\bibitem{tian1992stability}
G.~Tian, ``On stability of the tangent bundles of {F}ano varieties,'' {\em
Internat. J. Math}, vol.~3, no.~3, pp.~401--413, 1992.
\bibitem{Tian87}
G.~Tian, ``On {K}{\"a}hler-{E}instein metrics on certain {K}{\"a}hler manifolds
with $c_1 (m)> 0$,'' {\em Inventiones Mathematicae}, vol.~89, no.~2,
pp.~225--246, 1987.
\bibitem{rubinstein2008}
Y.~A. Rubinstein, ``Some discretizations of geometric evolution equations and
the {R}icci iteration on the space of {K}{\"a}hler metrics,'' {\em Advances
in Mathematics}, vol.~218, no.~5, pp.~1526--1565, 2008.
\bibitem{szekelyhidi2011}
G.~Sz{\'e}kelyhidi, ``Greatest lower bounds on the {R}icci curvature of {F}ano
manifolds,'' {\em Compositio Mathematica}, vol.~147, no.~1, pp.~319--331,
2011.
\bibitem{rubinstein2009}
Y.~Rubinstein, ``On the construction of {N}adel multiplier ideal sheaves and
the limiting behavior of the {R}icci flow,'' {\em Transactions of the
American Mathematical Society}, vol.~361, no.~11, pp.~5839--5850, 2009.
\bibitem{li2017}
C.~Li {\em et~al.}, ``K-semistability is equivariant volume minimization,''
{\em Duke Mathematical Journal}, vol.~166, no.~16, pp.~3147--3218, 2017.
\bibitem{li2011}
C.~Li, ``Greatest lower bounds on {R}icci curvature for toric {F}ano
manifolds,'' {\em Advances in Mathematics}, vol.~226, no.~6, pp.~4921--4932,
2011.
\bibitem{delcroix2017}
T.~Delcroix, ``{K}{\"a}hler--{E}instein metrics on group compactifications,''
{\em Geometric and Functional Analysis}, vol.~27, no.~1, pp.~78--129, 2017.
\bibitem{yao2017}
Y.~Yao, ``Greatest lower bounds on {R}icci curvature of homogeneous toric
bundles,'' {\em International Journal of Mathematics}, vol.~28, no.~04,
p.~1750024, 2017.
\bibitem{Matsushima}
Y.~{M}atsushima, ``Remarks on {K}{\"a}hler-{E}instein manifolds,'' {\em Nagoya
{M}ath. {J}.}, vol.~46, pp.~161--173, 1972.
\bibitem{li06}
L.~Li, ``Wonderful compactification of an arrangement of subvarieties,'' {\em
Michigan Math. J.}, vol.~58, no.~2, pp.~535--563, 2009.
\bibitem{suess18-2}
H.~S{\"u}{\ss}, ``{Orbit spaces of maximal torus actions on oriented
{G}rassmannians of planes}.'' 2018.
\bibitem{demailly2001}
J.-P. Demailly and J.~Koll{\'a}r, ``Semi-continuity of complex singularity
exponents and {K}{\"a}hler-{E}instein metrics on {F}ano orbifolds,'' in {\em
Annales scientifiques de l'Ecole normale sup{\'e}rieure}, vol.~34,
pp.~525--556, 2001.
\bibitem{cheltsov08}
I.~A. Cheltsov and K.~A. Shramov, ``Log canonical thresholds of smooth {F}ano
threefolds,'' {\em Russian Mathematical Surveys}, vol.~63, no.~5, p.~859,
2008.
\bibitem{shi2012kahler}
Y.~Shi and X.~Zhu, ``{K}{\"a}hler-{R}icci solitons on toric {F}ano orbifolds,''
{\em Mathematische Zeitschrift}, vol.~271, no.~3-4, pp.~1241--1251, 2012.
\end{thebibliography}