Anti-Pluricanonical Systems On Q-Fano Threefolds

TL;DR

This paper studies the birational properties of anti-pluricanonical maps on Q-Fano threefolds, aiming to understand when these maps are birational and their geometric implications.

Contribution

It provides new criteria and results on the birationality of anti-pluricanonical maps on Q-Fano threefolds, expanding understanding of their geometric structure.

Findings

Criteria for birationality of anti-pluricanonical maps

Conditions under which the maps are birational

Insights into the geometry of Q-Fano threefolds

Abstract

We investigate birationality of the anti-pluricanonical map $\phi_{-m}$, the rational map defined by the anti-pluricanonical system $|-mK|$, on $\mathbb{Q}$-Fano threefolds.