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<p>Working in the category of smooth projective varieties over an algebraically closed field of characteristic 0, we review notions of ampleness and numerical nefness for Higgs bundles which “feel” the Higgs field and formulate criteria of the Barton-Kleiman type for these notions. We give an application to minimal surfaces of general type that saturate the Miyaoka-Yau inequality, showing that their cotangent bundle is ample.</p>

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Positivity for Higgs Vector Bundles: Criteria and Applications

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2025年10月28日

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  • Ugo Bruzzo,
  • Armando Capasso,
  • Beatriz Graña Otero

摘要

Working in the category of smooth projective varieties over an algebraically closed field of characteristic 0, we review notions of ampleness and numerical nefness for Higgs bundles which “feel” the Higgs field and formulate criteria of the Barton-Kleiman type for these notions. We give an application to minimal surfaces of general type that saturate the Miyaoka-Yau inequality, showing that their cotangent bundle is ample.