Algebra and Geometry Seminar

Tian-Yau's seminal work in the 90s constructed complete Calabi-Yau metrics on the complement of a smooth anticanonical divisor inside a Fano manifold, with asymptotic geometry modelled on the Calabi ansatz. We generalise the construction to the case where the anticanonical divisor is the union of two transverse divisors, based on a generalised Calabi ansatz, which is motivated from polarised degenerations. Time permitting I may also discuss some (heuristic) relation to non-archimedean Monge-Ampere equation.