Geometry & Topology Volume 22, issue 7 (2018)

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An application of the Duistermaat–Heckman theorem and its extensions in Sasaki geometry

Charles P Boyer, Hongnian Huang and Eveline Legendre

Geometry & Topology 22 (2018) 4205–4234

DOI: 10.2140/gt.2018.22.4205

Bibliography

1	M F Atiyah, R Bott, The moment map and equivariant cohomology, Topology 23 (1984) 1 MR721448
2	M Audin, The topology of torus actions on symplectic manifolds, 93, Birkhäuser (1991) 181 MR1106194
3	N Berline, E Getzler, M Vergne, Heat kernels and Dirac operators, 298, Springer (1992) MR1215720
4	N Berline, M Vergne, Zéros d’un champ de vecteurs et classes caractéristiques équivariantes, Duke Math. J. 50 (1983) 539 MR705039
5	S Boucksom, J P Demailly, M Păun, T Peternell, The pseudo-effective cone of a compact Kähler manifold and varieties of negative Kodaira dimension, J. Algebraic Geom. 22 (2013) 201 MR3019449
6	C P Boyer, C van Coevering, Relative K–stability and extremal Sasaki metrics, Math. Res. Lett. 25 (2018) 1 MR3818612
7	C P Boyer, K Galicki, Sasakian geometry, Oxford Univ. Press (2008) MR2382957
8	C P Boyer, K Galicki, S R Simanca, Canonical Sasakian metrics, Comm. Math. Phys. 279 (2008) 705 MR2386725
9	C P Boyer, H Huang, E Legendre, C W Tønnesen-Friedman, The Einstein–Hilbert functional and the Sasaki–Futaki invariant, Int. Math. Res. Not. 2017 (2017) 1942 MR3658189
10	C P Boyer, C W Tønnesen-Friedman, Extremal Sasakian geometry on S³–bundles over Riemann surfaces, Int. Math. Res. Not. 2014 (2014) 5510 MR3271180
11	C P Boyer, C W Tønnesen-Friedman, The Sasaki join, Hamiltonian 2–forms, and constant scalar curvature, J. Geom. Anal. 26 (2016) 1023 MR3472828
12	T C Collins, G Székelyhidi, K–semistability for irregular Sasakian manifolds, J. Differential Geom. 109 (2018) 81 MR3798716
13	J P Demailly, Singular Hermitian metrics on positive line bundles, from: "Complex algebraic varieties" (editors K Hulek, T Peternell, M Schneider, F O Schreyer), Lecture Notes in Math. 1507, Springer (1992) 87 MR1178721
14	S K Donaldson, Scalar curvature and stability of toric varieties, J. Differential Geom. 62 (2002) 289 MR1988506
15	S K Donaldson, Constant scalar curvature metrics on toric surfaces, Geom. Funct. Anal. 19 (2009) 83 MR2507220
16	J J Duistermaat, G J Heckman, On the variation in the cohomology of the symplectic form of the reduced phase space, Invent. Math. 69 (1982) 259 MR674406
17	A Futaki, H Ono, G Wang, Transverse Kähler geometry of Sasaki manifolds and toric Sasaki–Einstein manifolds, J. Differential Geom. 83 (2009) 585 MR2581358
18	P Gauduchon, Calabi’s extremal Kähler metrics : an elementary introduction, book project (2015)
19	V Guillemin, S Sternberg, Convexity properties of the moment mapping, Invent. Math. 67 (1982) 491 MR664117
20	W He, S Sun, The generalized Frankel conjecture in Sasaki geometry, Int. Math. Res. Not. 2015 (2015) 99 MR3340296
21	G Heier, B Wong, Scalar curvature and uniruledness on projective manifolds, Comm. Anal. Geom. 20 (2012) 751 MR2981838
22	J Kollár, Einstein metrics on five-dimensional Seifert bundles, J. Geom. Anal. 15 (2005) 445 MR2190241
23	E Legendre, Existence and non-uniqueness of constant scalar curvature toric Sasaki metrics, Compos. Math. 147 (2011) 1613 MR2834736
24	E Lerman, Contact toric manifolds, J. Symplectic Geom. 1 (2003) 785 MR2039164
25	E Lerman, S Tolman, Hamiltonian torus actions on symplectic orbifolds and toric varieties, Trans. Amer. Math. Soc. 349 (1997) 4201 MR1401525
26	D Martelli, J Sparks, S T Yau, The geometric dual of a–maximisation for toric Sasaki–Einstein manifolds, Comm. Math. Phys. 268 (2006) 39 MR2249795
27	D Martelli, J Sparks, S T Yau, Sasaki–Einstein manifolds and volume minimisation, Comm. Math. Phys. 280 (2008) 611 MR2399609
28	D McDuff, D Salamon, Introduction to symplectic topology, Clarendon (1995) MR1373431
29	Y Miyaoka, S Mori, A numerical criterion for uniruledness, Ann. of Math. 124 (1986) 65 MR847952
30	J Ross, R Thomas, Weighted projective embeddings, stability of orbifolds, and constant scalar curvature Kähler metrics, J. Differential Geom. 88 (2011) 109 MR2819757
31	J Stoppa, K–stability of constant scalar curvature Kähler manifolds, Adv. Math. 221 (2009) 1397 MR2518643
32	G Tian, Kähler–Einstein metrics on algebraic manifolds, from: "Transcendental methods in algebraic geometry" (editors F Catanese, C Ciliberto), Lecture Notes in Math. 1646, Springer (1996) 143 MR1603624
33	B Watson, Manifold maps commuting with the Laplacian, J. Differential Geometry 8 (1973) 85 MR0365419