Geodesic
Limits of Calabi–Yau metrics when the Kähler class degenerates
Journal of the European Mathematical Society, Tome 11 (2009) no. 4, pp. 755-776.

Voir la notice de l'article provenant de la source EMS Press

We study the behavior of families of Ricci-flat Kähler metrics on a projective Calabi– Yau manifold when the Kähler classes degenerate to the boundary of the ample cone. We prove that if the limit class is big and nef the Ricci-flat metrics converge smoothly on compact sets outside a subvariety to a limit incomplete Ricci-flat metric. The limit can also be understood from algebraic geometry.
DOI : 10.4171/jems/165
Classification : 32-XX, 14-XX, 00-XX
Mots-clés : Calabi–Yau manifolds, Ricci-flat metrics, degenerate complex Monge–Ampère equations 
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     author = {Valentino Tosatti},
     title = {Limits of {Calabi{\textendash}Yau} metrics when the {K\"ahler} class degenerates},
     journal = {Journal of the European Mathematical Society},
     pages = {755--776},
     publisher = {mathdoc},
     volume = {11},
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     year = {2009},
     doi = {10.4171/jems/165},
     url = {https://geodesic-test.mathdoc.fr/articles/10.4171/jems/165/}
}
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Valentino Tosatti. Limits of Calabi–Yau metrics when the Kähler class degenerates. Journal of the European Mathematical Society, Tome 11 (2009) no. 4, pp. 755-776. doi : 10.4171/jems/165. https://geodesic-test.mathdoc.fr/articles/10.4171/jems/165/

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