grack


Gromov-Hausdorff Convergence in Kähler Geometry

[3 publications multipartenaires, 59 publications monopartenaires]

Articles

  • V. Apostolov, H. Auvray, L. Sektnan: Extremal Kähler Poincaré type metrics on toric varieties. J. Geom. Anal. 31, no. 2, 1223-1290 (2021).

  • V. Apostolov, D. Calderbank, P. Gauduchon, E. Legendre: Contact toric manifolds of arbitrairy codimension. Int. Math. Res. Not. 2020, No. 8, 2436-2467 (2020).

  • V. Apostolov, D. Calderbank, P. Gauduchon, E. Legendre: Levi-Kähler reduction of CR structures, products of spheres, and toric geometry. Math. Res. Lett. 27, 1565-1629 (2020).

  • V. Apostolov, D. Calderbank, E. Legendre: Weighted K-stability of polarized varieties and extremality of Sasaki manifolds. Adv. Math. 391 (2021).

  • H. Auvray, X. Ma, G. Marinescu: Bergman kernels on punctured Riemann surfaces. Math. Ann. 379, no. 3-4, 951-1002 (2021).

  • H. Auvray, X. Ma, G. Marinescu: Quotient of Bergman kernels on punctured Riemann surfaces. Math. Z. 301, 2339–2367 (2022).

  • R. Berman, S. Boucksom, M. Jonsson: A variational approach to the Yau-Tian-Donaldson conjecture . J. Amer. Math. Soc. 34, 605-652 (2021).

  • O. Biquard: Non dégénérescence et singularités des métriques d'Einstein asymptotiquement hyperboliques en dimension 4. Math. Ann. 372, No. 1-2, 531-553 (2018).

  • O. Biquard: Métriques hyperkählériennes pliées. Bull. Soc. Math. Fr. 147, No. 2, 303-340 (2019).

  • O. Biquard, T. Delcroix: Ricci flat Kähler metrics on rank two complex symmetric spaces. J. Éc. Polytech., Math. 6, 163-201 (2019).

  • O. Biquard, H. Guenancia: Degenerating Kähler-Einstein cones, locally symmetric cusps, and the Tian-Yau metric. To appear in Invent. Math. (arXiv)

  • S. Boucksom: Variational and non-Archimedean aspects of the Yau-Tian-Donaldson conjecture. Proc. ICM 2018 Rio de Janeiro, Vol. 1, 589-614.

  • S. Boucksom, S. Diverio: A note on Lang’s conjecture for quotients of bounded domains. Épijournal Géom. Algébrique 5 (2021).

  • S. Boucksom, D. Eriksson: Spaces of norms, determinant of cohomology and Fekete points in non-Archimedean geometry. Adv. Math. 378 (2021).

  • S. Boucksom, W. Gubler, F. Martin: Differentiability of relative volumes over an arbitrary non-Archimedean field. Int. Math. Res. Not. 2022, No. 8, 6214-6242 (2022).

  • S. Boucksom, W. Gubler, F. Martin: Non-Archimedean volumes of metrized nef line bundles. Épijournal de Géom. Algébr., EPIGA 5, Article 13, 34 p. (2021).

  • S. Boucksom, T. Hisamoto, M. Jonsson: Uniform K-stability and asymptotics of energy functionals in Kähler geometry. J. Eur. Math. Soc. 21, no. 9, 2905–2944 (2019).

  • S. Boucksom, M. Jonsson: Tropical and non-Archimedean limits of degenerating families of volume forms. J. Ec. Polytechnique 4 (2017), 87-139 (arXiv).

  • S. Boucksom, M. Jonsson: Global pluripotential theory over a trivially valued field. Ann. Fac. Sci. Toulouse Math. (6) 31 (2022), no. 3, 647-836.

  • C. Boyer, H. Huang, E. Legendre, C.W. Tønnesen-Friedman: Reducibility in Sasakian geometry. Trans. AMS. 370 (2018), 6825-6869 (arXiv).

  • C. Boyer, H. Huang, E. Legendre: An application of the Duistermaat-Heckman Theorem in Sasaki geometry. Geom. Topol. 22, 4205-4234 (2018) (arXiv).

  • B. Cadorel, S. Diverio, H. Guenancia: On subvarieties of singular quotients of bounded domains. J. London Math. Soc. online (arXiv).

  • F. Campana, J. Cao, S.I. Matsumura: Projective klt pairs with nef anti-canonical divisor. Algebr. Geom. 8, No. 4, 430-464 (2021).

  • J. Cao: Kodaira dimension of algebraic fiber spaces over surfaces. Algebr. Geom 5, 728-741 (2018).

  • J. Cao: Albanese maps of projective manifolds with nef anticanonical bundles. Ann. Sci. Éc. Norm. Supér. 52, No. 5, 1137-1154 (2019).

  • J. Cao, J.P. Demailly, S.I. Matsumura: A general extension theorem for cohomology classes on non reduced analytic spaces. Sci. China Math. 60 (2017) (arXiv).

  • J. Cao, H. Guenancia, M. Păun: Variation of singular Kähler-Einstein metrics: positive Kodaira dimension. J. Reine Angew. Math. 779, 1-36 (2021).

  • J. Cao, A. Höring A decomposition theorem for projective manifolds with nef anticanonical bundle. J. Algebr. Geom. 28, No. 3, 567-597 (2019).

  • J. Cao, A. Höring Rational curves on compact Kähler manifolds. J. Differ. Geom. 114, No. 1, 1-39 (2020).

  • G. Carron: Geometric inequalities for manifolds with Ricci curvature in the Kato class. Ann. Inst. Fourier 69, No. 7, 3095-3167 (2019).

  • G. Carron, C. Rose: Geometric and spectral estimates based on spectral Ricci curvature assumptions. J. Reine Angew. Math. 772, 121-145 (2021).

  • D. Coman, V. Guedj, S. Sahin, A. Zeriahi: Toric Pluripotential Theory. Ann. Pol. Math. 123, Part 1, 215-242 (2019).

  • M. De Borbon, E. Legendre: Toric Sasaki-Einstein metrics with conical singularities. Sel. Math., New Ser. 28, No. 3, Paper No. 64, 40 p. (2022).

  • J.P. Demailly, M.R. Rahmati: Morse cohomology estimates for jet differential operators. Boll. Unione Mat. Ital. 12, No. 1-2, 145-164 (2019).

  • J.P. Demailly: Extension of holomorphic functions defined on non reduced analytic subvarieties. The legacy of Bernhard Riemann after one hundred and fifty years. Vol. I, 191–222, Adv. Lect. Math. (ALM), 35.1, Int. Press, Somerville, MA, 2016 (arXiv).

  • J.P. Demailly: Fano manifolds with nef tangent bundles are weakly almost Kähler-Einstein. Asian J. Math. 22 (2018), no. 2, 285–290. (arXiv).

  • J.P. Demailly: Hermitian-Yang-Mills approach to the conjecture of Griffiths on the positivity of ample vector bundles. Mat. Sbornik 212, 39-53 (2021). (arXiv).

  • J.P. Demailly: Bergman bundles and applications to the geometry of compact complex manifolds. Pure Appl. Math. Q. 18, No. 1, 211-249 (2022).

  • S. Dinew, V. Guedj, A. Zeriahi: Open problems in pluripotential theory. Complex Var. Elliptic Equ. 61 (2016), no. 7, 902–930 (arXiv).

  • E. Di Nezza, V. Guedj: Geometry & Topology of the space of Kähler metrics on singular varieties. Compositio 154 (2018), 1593–1632. (arXiv).

  • E. Di Nezza, V. Guedj, H. Guenancia: Families of singular Kähler-Einstein metrics. To appear in J. Eur. Math. Soc. (arXiv).

  • E. Di Nezza, V. Guedj, H.C. Lu: Finite entropy vs finite energy. Comment. Math. Helv. 96 , 389–419 (2021) (arXiv).

  • S. Diverio: Segre forms and Kobayashi-Lübke inequality. Math. Z. 283 , no. 3-4, 1033–1047 (2016).

  • S. Diverio: Quasi-negative holomorphic sectional curvature and ampleness of the canonical class. Complex and symplectic geometry, 61–71, Springer INdAM Ser., 21, Springer, Cham, 2017.

  • S. Diverio: Limits in family of pseudoeffective classes. Appendix to the paper "Twisted Cotangent Bundles of Hyperkähler Manifolds", by F. Anella, A. Höring. J. Éc. polytech. Math. 8, 1429–1457 (2021).

  • S. Diverio, F. Fagioli: Pointwise Universal Gysin formulae and Applications towards Griffiths’ conjecture. To appear on Ann. Sc. Norm. Super. Pisa Cl. Sci. (arXiv).

  • S. Diverio, C. Fontanari, D. Martinelli: Rational curves on fibered Calabi–Yau manifolds. Doc. Math. 24, 663–675 (2019).

  • S. Diverio, S. Trapani: Quasi-negative holomorphic sectional curvature and positivity of the canonical bundle. J. Differential Geom. 111, no. 2, 303–314 (2019).

  • P. Eyssidieux, V. Guedj, A. Zeriahi: Convergence of weak Kähler-Ricci flows on minimal models of positive Kodaira dimension. Comm. Math. Phys. 357 (2018) 1179–1214 (arXiv).

  • P. Eyssidieux, V. Guedj, A. Zeriahi: Corrigendum: Viscosity solutions to complex Monge-Ampère equations. Comm. Pure Appl. Math. 70 (2017), no. 5, 815–821 (arXiv).

  • V. Guedj, H.C. Lu, A. Zeriahi: Plurisubharmonic envelopes and supersolutions. J. Differ. Geom. 113, No. 2, 273-313 (2019).

  • V. Guedj, H.C. Lu, A. Zeriahi: Weak subsolutions to complex Monge-Ampère equations. J. Math. Soc. Japan 71, No. 3, 727-738 (2019).

  • V. Guedj, H.C. Lu, A. Zeriahi: Pluripotential Kähler-Ricci flows. Geom. Topol. 24, No. 3, 1225-1296 (2020).

  • V. Guedj, H.C. Lu, A. Zeriahi: The pluripotential Cauchy-Dirichlet problem for complex Monge-Ampère flows. Ann. Sci. Éc. Norm. Supér. (4) 54, No. 4, 889-944 (2021).

  • V. Guedj, H.C. Lu, A. Zeriahi: Stability of solutions to complex Monge-Ampère flows. Ann. Inst. Fourier 68, No. 7, 2819-2836 (2018).

  • V. Guedj, S. Sahin, A. Zeriahi: Choquet-Monge-Ampère Classes. Potential Anal. 46 (2017), no. 1, 149–165 (arXiv).

  • E. Legendre: A note on extremal toric almost Kähler metrics. Codogni, Giulio (ed.) et al., Moduli of K-stable varieties. Cham: Springer. Springer INdAM Ser. 31, 53-74 (2019) (arXiv).

  • E. Legendre: Localizing the Donaldson-Futaki invariant. Int. J. Math. 32, No. 8 (2021).

  • E. Legendre, Y. Rollin: Hamiltonian stationary Lagrangian fibrations. J. Symplectic Geom. 17, No. 3, 753-791 (2019) (arXiv).

  • E. Legendre, R. Sena-Dias: Toric aspects of the first eigenvalue. J. Geom. Anal. 28, No. 3, 2395-2421 (2018).


Ouvrage

  • V. Guedj, A. Zeriahi: Degenerate complex Monge-Ampère equations. EMS Tracts in Mathematics, 26. European Mathematical Society (EMS), Zürich, 2017. xxiv+472 pp.


Preprints

  • O. Biquard, H. Macbeth: Steady Kähler-Ricci solitons on crepant resolutions of finite quotients of Cn. arXiv:1711.02019.

  • S. Boucksom, M. Jonsson: A non-Archimedean approach to K-stability, I: Metric geometry of spaces of test configurations and valuations. arXiv:1805.11160.



Thanks to the authors for adding up the mention "This project was partially supported by ANR GRACK, decision N° ANR-15-CE40-0003" on their various productions.

For (invited) communications of the members during the project, please follow this link.