Voir la notice de l'article provenant de la source Cambridge University Press
@article{10_1017_fmp_2023_5,
author = {Harold Blum and Yuchen Liu and Chenyang Xu and Ziquan Zhuang},
title = {The existence of the {K\"ahler{\textendash}Ricci} soliton degeneration},
journal = {Forum of Mathematics, Pi},
publisher = {mathdoc},
volume = {11},
year = {2023},
doi = {10.1017/fmp.2023.5},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.1017/fmp.2023.5/}
}
TY - JOUR AU - Harold Blum AU - Yuchen Liu AU - Chenyang Xu AU - Ziquan Zhuang TI - The existence of the Kähler–Ricci soliton degeneration JO - Forum of Mathematics, Pi PY - 2023 VL - 11 PB - mathdoc UR - http://geodesic.mathdoc.fr/articles/10.1017/fmp.2023.5/ DO - 10.1017/fmp.2023.5 LA - en ID - 10_1017_fmp_2023_5 ER -
Harold Blum; Yuchen Liu; Chenyang Xu; Ziquan Zhuang. The existence of the Kähler–Ricci soliton degeneration. Forum of Mathematics, Pi, Tome 11 (2023). doi: 10.1017/fmp.2023.5
[AZ22] and , ‘ K-stability of Fano varieties via admissible flags’, Forum Math. Pi. 10 (2022), Paper No. e15.Google Scholar | DOI
[Bam18] , ‘Convergence of Ricci flows with bounded scalar curvature’, Ann. of Math. (2) 188(3) (2018), 753–831.Google Scholar | DOI
[Ber16] , ‘K-polystability of -Fano varieties admitting Kähler–Einstein metrics’, Invent. Math. (3) (2016), 973–1025.Google Scholar | DOI
[BWN14] and , ‘Complex optimal transport and the pluripotential theory of Kähler–Ricci solitons’, Preprint, 2014, .Google Scholar | arXiv
[Ber15] , ‘A Brunn–Minkowski type inequality for Fano manifolds and some uniqueness theorems in Kähler geometry’, Invent. Math. 200(1) (2015), 149–200.Google Scholar | DOI
[BCHM10] , , and , ‘Existence of minimal models for varieties of log general type’, J. Amer. Math. Soc. 23(2) (2010), 405–468.Google Scholar | DOI
[BC11] and , ‘Okounkov bodies of filtered linear series’, Compos. Math. 147(4) (2011), 1205–1229.Google Scholar | DOI
[BE21] and , ‘Spaces of norms, determinant of cohomology and Fekete points in non-Archimedean geometry’, Adv. Math. 378 (2021), 107501, 124.Google Scholar | DOI
[BHJ17] , and , ‘Uniform K-stability, Duistermaat–Heckman measures and singularities of pairs’, Ann. Inst. Fourier (Grenoble) 67(2) (2017), 743–841.Google Scholar | DOI
[BJ21] and , ‘A non-Archimedean approach to K-stability, I: Metric geometry of spaces of test configurations and valuations’, Preprint, 2021, .Google Scholar | arXiv
[BJ20] and , ‘Thresholds, valuations, and K-stability’, Adv. Math. 365(2020), 107062, 57.Google Scholar | DOI
[BL22] and , ‘Openness of uniform K-stability in families of -Fano varieties’, Ann. Sci. Éc. Norm. Supér. (4) 55(1) (2022), 1–41.Google Scholar | DOI
[BLX22] , and , ‘Openness of K-semistability for Fano varieties’, Duke Math. J. 171 (13) (2022), 2753–2797.Google Scholar
[CM15] and , ‘Distribution of logarithmic spectra of the equilibrium energy’, Manuscripta Math. 146(3–4) (2015), 365–394.Google Scholar | DOI
[Che20] , ‘Boundedness of weak Fano pairs with alpha-invariants and volumes bounded below’, Publ. Res. Inst. Math. Sci. 56(3) (2020), 539–559 Google Scholar | DOI
[CSW18] , and , ‘Kähler–Ricci flow, Kähler–Einstein metric, and K-stability’, Geom. Topol. 22(6) (2018), 3145–3173.Google Scholar | DOI
[CW20] and , ‘Space of Ricci flows (II)—Part B: Weak compactness of the flows’, J. Differential Geom. 116(1) (2020), 1–123.Google Scholar | DOI
[DS16] and , ‘Kähler–Einstein metrics along the smooth continuity method’, Geom. Funct. Anal. 26(4) (2016), 975–1010.Google Scholar
[DS20] and , ‘The Kähler–Ricci flow and optimal degenerations’, J. Differential Geom. 116(1) (2020), 187–203.Google Scholar
[ELMNP] , , , and , ‘Restricted volumes and base loci of linear series’, Amer. J. Math. 131(3) (2009), 607–651.Google Scholar
[Fuj19] , ‘A valuative criterion for uniform K-stability of -Fano varieties’, J. Reine Angew. Math. 751 (2019), 309–338.Google Scholar | DOI
[Fuj19b] , ‘K-stability of Fano manifolds with not small alpha invariants’, J. Inst. Math. Jussieu 18(3( (2019), 519–530.Google Scholar | DOI
[He16] , ‘Kähler–Ricci soliton and -functional’, Asian J. Math. 20(4) (2016), 645–663.Google Scholar | DOI
[HL20] and , ‘On the Yau–Tian–Donaldson conjecture for generalized Kähler–Ricci soliton equations’, Preprint, 2020, , To appear in Comm. Pure Appl. Math.Google Scholar | arXiv
[HL20b] and , ‘Algebraic uniqueness of Kähler–Ricci flow limits and optimal degenerations of Fano varieties’, Preprint, 2020, . To appear in Geom. Topol.Google Scholar | arXiv
[HMX13] , and , ‘On the birational automorphisms of varieties of general type’, Ann. of Math. (2) 177(3) (2013), 1077–1111.Google Scholar | DOI
[Hor03] , The Analysis of Linear Partial Differential Operators. Distribution theory and Fourier analysis. Reprint of the second (1990) edition (Springer, Berlin; MR1065993). Classics in Mathematics. Springer-Verlag, Berlin, 2003. x+440 pp.Google Scholar
[Jia20] , ‘Boundedness of -Fano varieties with degrees and alpha-invariants bounded from below’, Ann. Sci. Éc. Norm. Supér. (4) 53(5) (2020), 1235–1248.Google Scholar
[JM12] and , ‘Valuations and asymptotic invariants for sequences of ideals’, Ann. Inst. Fourier (Grenoble) 62(6) (2012), 2145–2209.Google Scholar
[KK12] and , ‘Newton–Okounkov bodies, semigroups of integral points, graded algebras and intersection theory’, Ann. of Math. (2) 176(2) (2012), 925–978.Google Scholar
[Kol13] , Singularities of the Minimal Model Program, Cambridge Tracts in Mathematics, vol. 200 (Cambridge University Press, Cambridge, 2013). With a collaboration of Sándor Kovács.Google Scholar | DOI
[KM98] and , Birational Geometry of Algebraic Varieties, Cambridge Tracts in Mathematics, vol. 134 (Cambridge University Press, Cambridge, 1998). With the collaboration of C. H. Clemens and A. Corti; Ttranslated from the 1998 Japanese original.Google Scholar
[Laz04] , Positivity in Algebraic Geometry . II, Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge., vol. 49, Springer-Verlag, Berlin, 2004.Google Scholar
[LM09] and , ‘Convex bodies associated to linear series’, Ann. Sci. Éc. Norm. Supér. (4) 42(5) (2009), 783–835.Google Scholar | DOI
[Li17] , ‘ K-semistability is equivariant volume minimization’, Duke Math. J. 166(16) (2017), 3147–3218.Google Scholar | DOI
[Li22] , ‘ -uniform stability and Kähler–Einstein metrics on Fano varieties’, Invent. Math. 227(2) (2022), 661–744.Google Scholar | DOI
[LLX20] , and , A Guided Tour to Normalized Volume, Geometric Analysis, in Honor of Gang Tian’s 60th Birthday, Progr. Math., vol. 333 (Birkhäuser/Springer, Cham, 2020), 167–219.Google Scholar
[LWX21] , and , ‘Algebraicity of the metric tangent cones and equivariant K-stability’, J. Amer. Math. Soc. 34 (4) (2021), 1175–1214.Google Scholar | DOI
[LX14] and , ‘Special test configuration and K-stability of Fano varieties’, Ann. of Math. (2) 180(1) (2014), 197–232.Google Scholar
[LXZ22] , and , ‘Finite generation for valuations computing stability thresholds and applications to K-stability’, Ann. of Math. (2) 196(2) (2022), 507–566.Google Scholar | DOI
[Reb21] , ‘The space of finite-energy metrics over a degeneration of complex manifolds’, Preprint, 2021, .Google Scholar | arXiv
[Reb22] , ‘Plurisubharmonic geodesics in spaces of non-Archimedean metrics of finite energy’, J. Reine Angew. Math. 793 (2022), 59–103.Google Scholar | DOI
[RTZ21] , and , ‘Basis divisors and balanced metrics’, J. Reine Angew. Math. 778 (2021), 171–218.Google Scholar | DOI
[Tia97] , ‘Kähler–Einstein metrics with positive scalar curvature’, Invent. Math. 130(1) (1997), 1–37.Google Scholar | DOI
[TZZZ13] , , and , ‘Perelman’s entropy and Kähler–Ricci flow on a Fano manifold’, Trans. Amer. Math. Soc. 365(12) (2013), 6669–6695.Google Scholar
[TZ16] and , ‘Regularity of Kähler–Ricci flows on Fano manifolds’, Acta Math. 216(1) (2016), 127–176.Google Scholar | DOI
[WZ04] and , ‘Kähler–Ricci solitons on toric manifolds with positive first Chern class’, Adv. Math. 188(1) (2004), 87–103.Google Scholar | DOI
[Xu20] , ‘A minimizing valuation is quasi-monomial’, Ann. of Math. (2) 191(3) (2020), 1003–1030.Google Scholar | DOI
[Xu21] , ‘Towards finite generation of higher rational rank valuations’, Mat. Sb. 212(3) (2021), 157–174 (Russian).Google Scholar
[XZ20] and , ‘On positivity of the CM line bundle on K-moduli spaces’, Ann. of Math. (2) 192(3) (2020), 1005–1068.Google Scholar | DOI
[XZ21] and , ‘Uniqueness of the minimizer of the normalized volume function’, Camb. J. Math. 9(1) (2021), 149–176.Google Scholar | DOI
Cité par Sources :