Chern numbers of terminal threefolds

TL;DR

This paper proves that the change in the cube of the first Chern class during flips in the minimal model program for smooth threefolds is bounded by a constant depending only on the second Betti number.

Contribution

It establishes a uniform bound on the variation of Chern numbers during flips in the minimal model program for threefolds.

Findings

Bound on the difference of c_1^3 during flips

Dependence of the bound only on b_2(X)

Advances understanding of Chern number behavior in MMP

Abstract

Let X be a smooth threefold. We show that if $X_i\dashrightarrow X_{i+1}$ is a flip which appears in the $K_X$-MMP, then $c_1(X_i)^3-c_1(X_{i+1})^3$ is bounded by a constant depending only on $b_2(X)$.