Speaker: Hans-Joachim Hein

Title: Compact Calabi-Yau manifolds with isolated conical singularities

Abstract:
In joint work with Song Sun, we prove that there exist compact Ricci-flat Riemannian spaces with isolated conical singularities that are not of orbifold type, i.e. whose sectional curvature is unbounded from both sides. More precisely, we explicitly determine the metric tangent cones of weak solutions to the complex Monge-Ampère equation on certain singular Calabi-Yau projective varieties, proving that the cross-sections of these cones are smooth and that the weak solution converges polynomially to its tangent cone.