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<p>Let <i>f</i>: <i>X</i> → <i>C</i> be an elliptic fibration. We prove that if the fundamental group π<sub>1</sub>(<i>X</i>) of <i>X</i> is infinite, then there exists a positive integer <i>m</i> such that <i>H</i><sup>0</sup>(<i>X, S</i><sup><i>m</i></sup>Ω<Stack> <sub><i>X</i></sub> <sup>1</sup> </Stack>) ≠ 0. This answers a question of H. Esnault for an elliptic fibration.</p>

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Fundamental Group and Symmetric Differentials on an Elliptic Fibration

  • 期刊论文

  • 发表日期：

    2026年4月15日

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  • Wanyuan Xu

摘要

Let f: X → C be an elliptic fibration. We prove that if the fundamental group π1(X) of X is infinite, then there exists a positive integer m such that H0(X, SmΩ X 1 ) ≠ 0. This answers a question of H. Esnault for an elliptic fibration.