Nonexistence of decreasing equisingular approximations with logarithmic poles
arXiv:1506.04581
Abstract
In this article, we present that for any complex manifold whose dimension is bigger than one, there exists a multiplier ideal sheaf such that there don't exist equisingular weights with logarithmic poles, which are not smaller than the orginal weight. A direct consequence is the nonexistence of decreasing equisingular approximations with logarithmic poles.
5 pages, 0 figures. In this version, we consider Question 1.1 on compact Hermitian manifolds, and promote the main result to general complex manifolds (compact and noncompact)