Comptes Rendus
no. 1
Analytic geometry
A singular Demailly–Păun theorem

Presented by: Jean-Pierre Demailly

Tristan C. Collins1; Valentino Tosatti2
1 Department of Mathematics, Harvard University, 1 Oxford Street, Cambridge, MA 02138, United States
2 Department of Mathematics, Northwestern University, 2033 Sheridan Road, Evanston, IL 60208, United States
Comptes Rendus. Mathématique, Volume 354 (2016) no. 1, pp. 91-95.

We give a numerical characterization of the Kähler cone of a possibly singular compact analytic variety that is embedded in a smooth ambient space.

On donne une caractérisation numérique du cône kählérien d'une variété analytique compacte qui est plongée dans un espace ambiant lisse.

Received:
Accepted:
Published online:
DOI: 10.1016/j.crma.2015.10.012

Tristan C. Collins 1; Valentino Tosatti 2

1 Department of Mathematics, Harvard University, 1 Oxford Street, Cambridge, MA 02138, United States
2 Department of Mathematics, Northwestern University, 2033 Sheridan Road, Evanston, IL 60208, United States 
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Tristan C. Collins; Valentino Tosatti. A singular Demailly–Păun theorem. Comptes Rendus. Mathématique, Volume 354 (2016) no. 1, pp. 91-95. doi : 10.1016/j.crma.2015.10.012. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2015.10.012/

[1] F. Campana; T. Peternell Algebraicity of the ample cone of projective varieties, J. Reine Angew. Math., Volume 407 (1990), pp. 160-166

[2] I. Chiose The Kähler rank of compact complex manifolds, J. Geom. Anal. (2015) (in press) | DOI

[3] T. Collins; V. Tosatti Kähler currents and null loci, Invent. Math., Volume 202 (2015) no. 3, pp. 1167-1198

[4] R.J. Conlon; H.-J. Hein Asymptotically conical Calabi–Yau manifolds, I, Duke Math. J., Volume 162 (2013) no. 15, pp. 2855-2902

[5] R.J. Conlon; H.-J. Hein Asymptotically conical Calabi–Yau manifolds, III (preprint) | arXiv

[6] J.-P. Demailly, Complex analytic and differential geometry, available on the author's webpage.

[7] J.-P. Demailly; M. Păun Numerical characterization of the Kähler cone of a compact Kähler manifold, Ann. of Math. (2), Volume 159 (2004) no. 3, pp. 1247-1274

[8] S.L. Kleiman Toward a numerical theory of ampleness, Ann. of Math. (2), Volume 84 (1966), pp. 293-344

[9] M. Păun Sur l'effectivité numérique des images inverses de fibrés en droites, Math. Ann., Volume 310 (1998) no. 3, pp. 411-421

[10] R. Richberg Stetige streng pseudokonvexe Funktionen, Math. Ann., Volume 175 (1968), pp. 257-286

[11] P.A.N. Smith Smoothing plurisubharmonic functions on complex spaces, Math. Ann., Volume 273 (1986) no. 3, pp. 397-413

[12] J. Varouchas Kähler spaces and proper open morphisms, Math. Ann., Volume 283 (1989) no. 1, pp. 13-52

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