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<p>The classical Mumford stability condition of vector bundles on a complex elliptic curve <i>X</i>, can be viewed as a Bridgeland stability condition on <i>D</i><sup><i>b</i></sup> (Coh <i>X</i>), the bounded derived category of coherent sheaves on <i>X</i>. This point of view gives us infinitely many <i>t</i>-structures and hearts on <i>D</i><sup><i>b</i></sup> (Coh <i>X</i>). In this paper, we answer the question which of these hearts are Noetherian or Artinian.</p>

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Different Hearts on Elliptic Curves

  • 期刊论文

  • 发表日期：

    2025年1月24日

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  • Yucheng Liu

摘要

The classical Mumford stability condition of vector bundles on a complex elliptic curve X, can be viewed as a Bridgeland stability condition on Db (Coh X), the bounded derived category of coherent sheaves on X. This point of view gives us infinitely many t-structures and hearts on Db (Coh X). In this paper, we answer the question which of these hearts are Noetherian or Artinian.