# A General Non-Vanishing Theorem and an Analytic Proof of the Finite Generation of the Canonical Ring

Research paper by Yum-Tong Siu

Indexed on: 25 Oct '06Published on: 25 Oct '06Published in: Mathematics - Algebraic Geometry

#### Abstract

On August 5, 2005 in the American Mathematical Society Summer Institute on Algebraic Geometry in Seattle and later in several conferences I gave lectures on my analytic proof of the finite generation of the canonical ring for the case of general type. After my lectures many people asked me for a copy of the slides which I used for my lectures. Since my slides were quite sketchy because of the time limitation for the lectures, I promised to post later on a preprint server my detailed notes from which my slides were extracted. Here are my detailed notes giving the techniques and the proof.