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 Cet article a éte moissonné depuis la source EMS Press

Voir la notice de l'article

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
Keywords: Calabi–Yau manifolds, Ricci-flat metrics, degenerate complex Monge–Ampère equations 
@article{JEMS_2009_11_4_a1,
     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},
     year = {2009},
     volume = {11},
     number = {4},
     doi = {10.4171/jems/165},
     url = {http://geodesic.mathdoc.fr/articles/10.4171/jems/165/}
}
TY  - JOUR
AU  - Valentino Tosatti
TI  - Limits of Calabi–Yau metrics when the Kähler class degenerates
JO  - Journal of the European Mathematical Society
PY  - 2009
SP  - 755
EP  - 776
VL  - 11
IS  - 4
UR  - http://geodesic.mathdoc.fr/articles/10.4171/jems/165/
DO  - 10.4171/jems/165
ID  - JEMS_2009_11_4_a1
ER  - 
%0 Journal Article
%A Valentino Tosatti
%T Limits of Calabi–Yau metrics when the Kähler class degenerates
%J Journal of the European Mathematical Society
%D 2009
%P 755-776
%V 11
%N 4
%U http://geodesic.mathdoc.fr/articles/10.4171/jems/165/
%R 10.4171/jems/165
%F JEMS_2009_11_4_a1
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

Cité par Sources :