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 Chern numbers. As an application, we prove that given $$R\in {\mathbb {R}}_{>0}$$ 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 $$4c_2(X,D)-c_1^2(X,D)\le R$$ , forms a bounded family.