A remark on the effective nonvanishing of Calabi–Yau varieties | Synapse
September 30, 2025Open Access
A remark on the effective nonvanishing of Calabi–Yau varieties
Key Points
The pluricanonical system in Calabi–Yau varieties is proven to be non-empty under certain conditions.
A positive integer related to natural invariants reflects on the fiber properties associated with the Albanese map.
Natural invariants play a crucial role in identifying effective nonvanishing in algebraic geometry.
This result enhances the understanding of Calabi–Yau varieties within the context of their algebraic properties.
Abstract
For a Calabi–Yau variety X, we prove that there exists a positive integer m, depending on two natural invariants of the fiber of its Albanese map, such that the pluricanonical system |mK X | is non-empty.