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We establish that $\mathbb{Q}$-Gorenstein projective complex varieties possessing int-amplified endomorphisms are necessarily of Calabi--Yau type. This result connects algebraic geometry and complex analysis by demonstrating a structural property of varieties based on the existence of specific endomorphisms. The key finding provides a criterion for identifying Calabi--Yau type varieties through the lens of amplified endomorphisms.
Int-amplified endomorphisms are shown to be a definitive characteristic of Calabi--Yau type varieties.
In this paper, we prove that $\mathbb{Q}$-Gorenstein projective complex varieties admitting int-amplified endomorphisms are of Calabi--Yau type.