# Non-vanishing theorem for log canonical pairs - Mathematics > Algebraic Geometry

Non-vanishing theorem for log canonical pairs - Mathematics > Algebraic Geometry - Download this document for free, or read online. Document in PDF available to download.

Abstract: We obtain a correct generalization of Shokurov-s non-vanishing theorem forlog canonical pairs. It implies the base point free theorem for log canonicalpairs. We also prove the rationality theorem for log canonical pairs. As acorollary, we obtain the cone theorem for log canonical pairs. We do not needAmbro-s theory of quasi-log varieties.

Author: ** Osamu Fujino**

Source: https://arxiv.org/