Smooth asymptotics for collapsing Calabi-Yau metrics

Abstract: I will present recent joint work with Valentino Tosatti in which we obtain a complete asymptotic expansion (locally uniformly away from the singular fibers) of Calabi-Yau metrics collapsing along a holomorphic fibration of a fixed compact Calabi-Yau manifold. The result is weaker than a standard asymptotic expansion in that the coefficient functions might still depend on the small parameter in some unknown way in the base variables. However, it is far stronger in that all terms including the remainder at each order are proved to be uniformly bounded in C^k for all k. We also calculate the first nontrivial coefficient in terms of the Kodaira-Spencer forms of the fibration.

differential geometry

Audience: researchers in the topic

B.O.W.L Geometry Seminar