Effective basepoint-free theorem for semi-log canonical surfaces

TL;DR

This paper establishes an effective basepoint-free theorem for semi-log canonical surfaces, extending Fujita-type conjectures and providing new results on very ampleness and freeness for various classes of algebraic surfaces.

Contribution

It proves a Fujita-type freeness conjecture for semi-log canonical pairs on curves and surfaces using quasi-log schemes, and offers effective results for stable, Fano, and log surfaces.

Findings

Proved the conjecture for curves and surfaces.

Derived effective very ampleness results for stable and semi-log canonical Fano surfaces.

Established an effective freeness result for log surfaces.

Abstract

This paper proposes a Fujita-type freeness conjecture for semi-log canonical pairs. We prove it for curves and surfaces by using the theory of quasi-log schemes and give some effective very ampleness results for stable surfaces and semi-log canonical Fano surfaces. We also prove an effective freeness for log surfaces.