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<p>We focus on the Schofield sequences over weighted projective lines in the sense of Geigle and Lenzing. We give a classification of all the Schofield sequences whose middle terms are line bundles or extension bundles for any weight type (2, 2, <i>n</i>). In particular, for the latter case such Schofield sequences are related to the distinguished exact structure on the subcategory of vector bundles. More precisely, the projective covers and injective hulls of extension bundles will provide Schofield sequences, and all the Schofield sequences in the subcategory of vector bundles can be obtained in this way.</p>

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Schofield sequences for weighted projective lines of type (2, 2, n)

  • 期刊论文

  • 发表日期：

    2025年5月21日

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  • Xiaofeng Zhang

摘要

We focus on the Schofield sequences over weighted projective lines in the sense of Geigle and Lenzing. We give a classification of all the Schofield sequences whose middle terms are line bundles or extension bundles for any weight type (2, 2, n). In particular, for the latter case such Schofield sequences are related to the distinguished exact structure on the subcategory of vector bundles. More precisely, the projective covers and injective hulls of extension bundles will provide Schofield sequences, and all the Schofield sequences in the subcategory of vector bundles can be obtained in this way.