Bounding singular surfaces via Chern numbers

Abstract

We prove the existence of a bound on the number of steps of the minimal model program for singular surfaces in terms of discrepancies and top Chern numbers. As an application, we prove that given $R\in\mathbb{R}$ and $\epsilon\in (0,1)$, the class $\mathcal{F}(R,\epsilon)$ of $2$-dimensional pairs $(X,D)$ of general type with $\epsilon$-klt singularities, $D$ with standard coefficients, and $4c_2(X,D)-c_1^2(X,D)\leq R$, forms a bounded family.