Differential Forms Around a Singularity

Abstract

In this chapter, we study the singularity by looking at the poles of the pull-back of differential forms around the singularity onto the resolved space. By this consideration, plurigenera of isolated singularities are defined and the order of growth of the plurigenera gives a rough classification of isolated singularities. Here, a variety is always integral and defined over the complex number field $\mathbb {C}$.

An attractive conjecture cannot be proved.

A big theorem’s proof is wrong.

If the proof is correct, the statement is trivial.