Gromov-Haudorff convergence of Kahler manifolds and the finite generation conjecture

Gromov-Haudorff convergence of Kahler manifolds and the finite generation conjecture

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Gang Liu, U.C. Berkeley
Fine Hall 314

We study the uniformization conjecture of Yau by using the Gromov-Haudorff convergence. As a consequence, we confirm Yau's finite generation conjecture. More precisely, on a complete noncompact Kahler manifold ith nonnegative bisectional curvature, the ring of polynomial growth holomorphic functions is finitely generated.  During the course, we prove if M is a complete noncompact Kahler manifold with nonnegative bisectional curvature and maximal volume growth, then it is biholomorphic to an affine algebraic variety. We also confirm a conjecture of Ni on the equivalence of several conditions on complete Kahler manifolds with nonnegative bisectional curvature.