Number of singular points on projective surfaces

TL;DR

This paper establishes an upper bound on the number of singular points on klt Fano surfaces, relating it to the Picard number, thereby advancing understanding of surface singularities in algebraic geometry.

Contribution

It provides a new bound on singular points for klt Fano surfaces based on their Picard number, a novel result in the classification of algebraic surfaces.

Findings

Number of singular points on klt Fano surfaces is at most 2 times the Picard number plus 2.

The bound links surface singularities directly to their Picard number.

The result improves classification constraints for algebraic surfaces.

Abstract

The number of singular points on a klt Fano surface $X$ is $\leq 2\rho(X)+2$.