Henri Guenancia's Webpage


  1. Diameter of Kähler currents (with V. Guedj and A. Zeriahi)
  2. Geometry of K-trivial Moishezon manifolds : decomposition theorem and holomorphic geometric structures (with I. Biswas, J. Cao and S. Dumitrescu)
  3. Strict positivity of Kähler-Einstein currents (with V. Guedj and A. Zeriahi)
    Forum of Mathematics, Sigma, to appear
  4. Equality in the Miyaoka-Yau inequality and uniformization of non-positively curved klt pairs (with B. Claudon and P. Graf)
    C. R Math. Acad. Sci. Paris, memorial volume for Jean-Pierre Demailly, to appear.
  5. Numerical characterisation of complex torus quotients (with B. Claudon and P. Graf)
    Comment. Math. Helv. 97, n°4, 769-799 (2022) [journal version]
  6. Degenerating Kähler-Einstein cones, locally symmetric spaces, and the Tian-Yau metric (with O. Biquard)
    Invent. Math. 230, 1101-1163 (2022) [journal version]
  7. Curvature formula for direct images of twisted relative canonical bundles endowed with a singular metric (with J. Cao and M. Păun)
    Ann. Fac. Sci. Toulouse Math. (6) 31 (2022), n°3, 861-905 [journal version]
  8. Continuity of singular Kähler-Einstein potentials (with V. Guedj and A. Zeriahi)
    IMRN 2023, n°2, 1355-1377 (2023) [journal version]
  9. Algebraic approximation and the decomposition theorem for Kähler Calabi-Yau varieties (with B. Bakker and C. Lehn)
    Invent. Math. 228, 1255–1308 (2022) [journal version]
  10. Kähler spaces with zero first Chern class: Bochner principle, Albanese maps and fundamental groups (with B. Claudon, P. Graf and P. Naumann)
    J. Reine Angew. Math. 786 (2022), 245-275 [journal version]
  11. A decomposition theorem for Q-Fano Kähler-Einstein varieties (with S. Druel and M. Păun)
    C. R Math. Acad. Sci. Paris, memorial volume for Jean-Pierre Demailly, to appear.
  12. Families of singular Kähler-Einstein metrics (with E. Di Nezza and V. Guedj)
    J. Eur. Math. Soc. 25, n°2, 633-679 (2023) [journal version]
  13. Variation of singular Kähler-Einstein metrics: Kodaira dimension zero (with J. Cao and M. Păun, appendix by V. Tosatti)
    J. Eur. Math. Soc. 25, n°2, 633-679 (2023) [journal version]
  14. On subvarieties of singular quotients of bounded domains (with B. Cadorel and S. Diverio)
    J. London. Math. Soc. (2) 2022; 106; 3208-3239 [journal version]
  15. A Bochner principle and its applications to Fujiki class C manifolds with vanishing first Chern class (with I. Biswas and S. Dumitrescu),
    Commun. Contemp. Math. 22 (2020), n°6, 1950051, 21 pp. [journal version]
  16. Quasi-projective manifolds with negative holomorphic sectional curvature
    Duke Math. J. 171 (2), 417-442 (2022) [journal version]
  17. Variation of singular Kähler-Einstein metrics: positive Kodaira dimension (with J. Cao and M. Păun)
    J. Reine Angew. Math. 779, 1-36 (2021) [journal version]
  18. A decomposition theorem for smoothable varieties with trivial canonical class (with S. Druel)
    J. Éc. polytech. Math. 5 (2018), p. 117-147 [journal version]
  19. Klt varieties with trivial canonical class: holonomy groups, differential forms and fundamental groups (with D. Greb and S. Kebekus)
    Geometry & Topology 23, n°4, 2051–2124 (2019) [journal version]
  20. Orbifold stability and Miyaoka-Yau inequality for minimal models (with B. Taji)
    Geometry & Topology 26, n°4, 1435-1482 (2022) [journal version]
  21. Families of conic Kähler-Einstein metrics
    Math. Annalen 376 (1), 1-37 (2020) [journal version]
  22. Kähler-Einstein metrics: from cones to cusps
    J. Reine Angew. Math. 759, 1-27 (2020) [journal version]
  23. Semi-stability of the tangent sheaf of singular varieties
    Algebraic Geometry, Vol 3, Issue 5 (2016), 508-542 [journal version]
  24. On the boundary behavior of Kähler-Einstein metrics on log canonical pairs (with D. Wu)
    Math. Annalen 366 (1), 101-120 (2016) [journal version]
  25. Kähler-Einstein metrics with conic singularities along self-intersecting divisors
    IMRN Vol. 2016, No. 15, 4634-4648 [journal version]
  26. Conic singularities metrics with prescribed Ricci curvature: the case of general cone angles along normal crossing divisors (with M. Paun)
    J. Differential Geom. 103, n°1 (2016), 15-57 [journal version]
  27. Kähler-Einstein metrics on stable varieties and log canonical pairs (with R. Berman)
    Geometric and Functional Analysis 24 (6), 1683-1730 (2014) [journal version]
  28. Kähler-Einstein metrics with cone singularities on klt pairs
    Int. J. Math. 24 1350035 (2013) [journal version]
  29. Kähler-Einstein metrics with mixed Poincaré and cone singularities along a normal crossing divisor
    Ann. Inst. Fourier 64 (3), 1291-1330 (2014) [journal version]
  30. Metrics with cone singularities along normal crossing divisors and holomorphic tensors fields (with F. Campana and M. Păun)
    Ann. Sci. Éc. Norm. Sup. 46 (2013), 879-916 [journal version]
  31. Toric plurisubharmonic functions and analytic adjoint ideal sheaves
    Math. Z. 271 (2012), 1011-1035 [erratum] [journal version]


  • Geometric applications of singular Kähler-Einstein metrics, text, Habilitation à Diriger des Recherches, defended on November 22, 2022
  • Klt varieties with trivial first Chern class, text, Summer school Foliations in Algebraic Geometry, Grenoble, July 2019
  • Métriques de Kähler-Einstein singulières, text, PhD Thesis supervised by S. Boucksom and M. Paun and defended on October 13, 2013
  • Points de vue algébriques et analytiques sur la notion de positivité en géométrie complexe, text, magister’s project, defended at the ENS in June 2010
  • Méthodes analytiques pour l’étude des singularités en géométrie complexe, text, master’s thesis, defended at Université Paris VI in June 2010