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In this paper, we study a fundamental property of a locally constant fibration \(f :X \rightarrow Y\) between smooth projective varieties. As an application, we prove that if the fiber F is rationally connected and the canonical divisor \(K_Y\) of the base Y is numerically trivial, then the Kodaira dimension and the numerical dimension of the anti-canonical divisor \(-K_F\) of F are greater than or equal to those of the anti-canonical divisor \(-K_X\) of X.

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Remarks on Locally Constant Fibrations over Projective Varieties of Calabi-Yau Type

  • 会议论文

  • 发表日期：

    2025年

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  • Shin-ichi Matsumura

摘要

In this paper, we study a fundamental property of a locally constant fibration \(f :X \rightarrow Y\) between smooth projective varieties. As an application, we prove that if the fiber F is rationally connected and the canonical divisor \(K_Y\) of the base Y is numerically trivial, then the Kodaira dimension and the numerical dimension of the anti-canonical divisor \(-K_F\) of F are greater than or equal to those of the anti-canonical divisor \(-K_X\) of X.