## On a Chern Number Inequality in Dimension 3

J. Math. Sci. Univ. Tokyo
Vol. 27 (2020), No. 1, Page 87-107.

Chen, Jheng-Jie
On a Chern Number Inequality in Dimension 3
We prove $c_1(X)\cdot c_2(X)< c_1(X^+)\cdot c_2(X^+)$ if $X$ --> $X^+$ is a 3-fold terminal flip (resp. $c_1(X)\cdot c_2(X)\leq c_1(Y)\cdot c_2(Y)$ if $X\to Y$ is a 3-fold elementary contraction contracting a divisor to a curve), where $c_1(X)$ and $c_2(X)$ denote the Chern classes. These provide affirmative answers to two questions by Xie in [Xie].