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This is a Quantitative Study study.

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.

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Cite This Study

Y. S. Zhu (Mon,) studied this question.

synapsesocial.com/papers/68dc1e308a7d58c25ebb1361 https://doi.org/https://doi.org/10.5802/crmath.735

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