Bounding singular surfaces via Chern numbers

2017/04/30 by Moraga, Joaquín
#Algebraic Geometry (math.AG) #FOS: Mathematics #Primary 14E30 #Secondary: 14J17

paper · doi:10.48550/arxiv.1705.00256

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∈ℝ and ε∈ (0,1), the class F(R,ε) of 2-dimensional pairs (X,D) of general type with ε-klt singularities, D with standard coefficients, and 4c₂(X,D)-c₁²(X,D)≤ R, forms a bounded family.

Related

• Orbifold Chern classes inequalities and applications
• Interaction Between Singularity Theory and the Minimal Model Program
• Singular Patterns of Generic Maps of Surfaces with Boundary into the Plane
• Optimal bounds for many T-singularities in stable surfaces
• Open surfaces of small volume