On Chern number inequality in dimension 3

Abstract

We prove that if $X--->X^{+}$ is a threefold terminal flip, then $c_1(X).c_2(X)\le c_1(X^{+}).c_2(X^{+})$ where $c_1(X)$ and $c_2(X)$ denote the Chern classes. This gives the affirmative answer to a Question by Xie \cite{Xie2}. We obtain the similar but weaker result in the case of divisorial contraction to curves.

21 pages, comments are welcome