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Seminários do IMPA

Geometria Diferencial

Título
Gromov-Hausdorff limits of Ricci-flat metrics on K3
Expositor
Misha Verbitsky

IMPA
Data
Terça-feira, 4 de fevereiro de 2020, 15:30
Local
Sala 236.
Resumo

Let W be the space of all Ricci-flat Kahler (that is, hyperkahler) metrics on a K3 surface $(M,I)$. Gromov defined a metric on a space of all metric spaces, called Gromov-Hausdorff metric. He proved that the set of Ricci-flat metrics of a given diameter on a given compact manifold has compact closure in the Gromov-Hausdorff space of metric spaces. I will show that the set of Gromov-Hausdorff limits of points in W contains any hyperkahler metric on M. This is surprizing, because dimension of W is 20, and dimension of the space of hyperkahler metrics on K3 is 58.