Extremal metrics on blowups

• Autores: Claudio Arezzo, Frank Pacard, Michael F. Singer
• Localización: Duke Mathematical Journal, ISSN 0012-7094, Vol. 157, Nº. 1, 2011, págs. 1-51
• Idioma: inglés
• DOI: 10.1215/00127094-2011-001
• Texto completo no disponible (Saber más ...)
• Referencias bibliográficas
  • C. Arezzo and F. Pacard, Blowing up and desingularizing constant scalar curvature Kähler orbifolds, Acta Math. 196 (2006), 179–228.
  • C. Arezzo and F. Pacard, Blowing up Kähler manifolds with constant scalar curvature, II, Ann. of Math. (2) 170 (2009), 685–738.
  • S. Bochner and W. T. Martin, Several Complex Variables, Princeton Math. Ser. 10, Princeton Univ. Press, Princeton, 1948.
  • E. Calabi, “Extremal Kähler metrics” in Seminar on Differential Geometry, Ann. of Math. Stud. 102, Princeton Univ. Press, Princeton, 1982,...
  • X. Chen, C. Lebrun, and B. Weber, On conformally Kähler Einstein manifolds, J. Amer. Math. Soc. 21 (2008), 1137–1168.
  • X. X. Chen and G. Tian, Geometry of Kähler metrics and foliations by holomorphic discs, Publ. Math. Inst. Hautes Études Sci. 107 (2008), 1–107.
  • A. Della Vedova, CM-stability of blow-ups and canonical metrics, preprint, arXiv:0810.5584v1 [math.AG].
  • S. K. Donaldson, Scalar curvature and stability of toric varieties, J. Differential Geom. 62 (2002), 289–349.
  • S. K. Donaldson, Interior estimates for solutions of Abreu’s equation, Collect. Math. 56 (2005), 103–142.
  • S. K. Donaldson, Extremal metrics on toric surfaces: A continuity method, J. Differential Geom. 79 (2008), 389–432.
  • S. K. Donaldson, Constant scalar curvature metrics on toric surfaces, Geom. Funct. Anal. 19 (2009), 83–136.
  • W. Fulton, Introduction to Toric Varieties, Ann. of Math. Stud. 131, Princeton Univ. Press, Princeton, 1993.
  • R. Hartshorne, Algebraic Geometry, Grad. Texts in Math. 52, Springer, New York, 1977.
  • W. He, Remarks on the existence of bilaterally symmetric extremal Kähler metrics on $\mathbb{CP}^2#2\overline{\mathbb{CP}}{}^2$, Int. Math....
  • F. C. Kirwan, Cohomology of Quotients in Symplectic and Algebraic Geometry, Math. Notes 31 (1984), Princeton Univ. Press, Princeton, 1984.
  • C. LeBrun, Counter-examples to the generalized positive action conjecture, Comm. Math. Phys. 118 (1988), 591–596.
  • C. LeBrun and S. Simanca, “On the Kähler classes of extremal metrics” in Geometry and Global Analysis (Sendai, Japan, 1993), Tohoku Univ.,...
  • C. LeBrun, Extremal Kähler metrics and complex deformation theory, Geom. Funct. Anal. 4 (1994), 298–336.
  • M. Levine, A remark on extremal Kähler metrics, J. Differential Geom. 21 (1985), 73–77.
  • R. B. Lockhart and R. C. McOwen, Elliptic differential operators on noncompact manifolds, Ann. Scuola Norm. Sup. Pisa Cl. Sci. (4) 12 (1985),...
  • T. Mabuchi, Stability of extremal Kähler manifolds, Osaka J. Math. 41 (2004), 563–582.
  • R. Mazzeo, Elliptic theory of differential edge operators, I, Comm. Partial Differential Equations 16 (1991), 1615–1664.
  • R. B. Melrose, The Atiyah-Patodi-Singer Index Theorem, Res. Notes Math. 4, A. K. Peters, Wellesley, Mass., 1993.
  • D. Mumford, J. Fogarty, and F. Kirwan, Geometric Invariant Theory, 3rd ed., Ergeb. Math. Grenzgeb. 34, Springer, Berlin, 1994.
  • S. R. Simanca, Kähler metrics of constant scalar curvature on bundles over $\mathbb{CP}_{n-1}$, Math. Ann. 291 (1991), 239–246.
  • Y. T. Siu, The existence of Kähler-Einstein metrics on manifolds with positive anticanonical line bundle and a suitable symmetry group, Ann....
  • G. Székelyhidi, Extremal metrics and K-stability, Bull. Lond. Math. Soc. 39 (2007), 76–84.
  • G. Tian, Extremal metrics and geometric stability, Houston J. Math. 28 (2002), 411–432.
  • G. Tian and S.-T. Yau, Kähler-Einstein metrics on complex surfaces with $c_1 > 0$, Comm. Math. Phys. 112 (1987), 175–203.