國立清華大學 數學系

Abstract:
We introduce in this talk a class of ``residue functions'', each of which ``deforms'' holomorphically certain weighted $L^2$ norm on the ambient complex manifold $X$ to an $L^2$ norm on the union of certain log-canonical (lc) centres of a given lc pair $(X,D)$. The properties of such residue functions can be encoded into a sequence of analytic adjoint ideal sheaves, which fit into various residue short exact sequences and are useful in facilitating induction on (co)dimension of lc centres in geometric problems involving lc singularities. As an illustration, we will see their use in a solution to Fujino's conjecture, that is, the injectivity theorem for lc pairs on compact Kähler manifolds. The content of this talk is based on the joint work with Young-Jun Choi and Shin-ichi Matsumura.