Fujita's Freeness Conjecture for $T$-Varieties of Complexity One

TL;DR

This paper proves Fujita's freeness conjecture for a specific class of algebraic varieties called Gorenstein complexity-one T-varieties with rational singularities, advancing understanding in algebraic geometry.

Contribution

It establishes the conjecture for a new class of varieties, specifically Gorenstein complexity-one T-varieties with rational singularities.

Findings

Fujita's freeness conjecture holds for Gorenstein complexity-one T-varieties.

The proof applies to varieties with rational singularities.

Advances the classification of varieties satisfying the conjecture.

Abstract

We prove Fujita's freeness conjecture for Gorenstein complexity-one $T$-varieties with rational singularities.