Scholarlink

<p>We generalise the notions of scalar-valued holomorphic <i>p</i>-contact and <i>s</i>-symplectic structures introduced recently on compact complex manifolds by the second-named author jointly with H. Kasuya and L. Ugarte to their analogues with values in a holomorphic line bundle. We then study the resulting holomorphic <i>p</i>-contact and <i>s</i>-symplectic manifolds which, unlike their scalar counterparts that are never Kähler, can even be projective. In particular, we investigate the (lack of) positivity properties of the canonical bundle of these manifolds when it is given a possibly singular Hermitian fibre metric. One of the tools used is a very recent regularisation result for <i>m</i>-psh functions obtained jointly by S. Dinew and the second-named author.</p>

错误：搜索内容不能为空，请输入英文关键词
错误：关键词超出字数限制，请精简
高级检索

Holomorphic p-Contact and s-Symplectic Line Bundles

  • 期刊论文

  • 出版模式：

    开放获取

  • 发表日期：

    2026年3月12日

查看全文
  • Kyle Broder,
  • Dan Popovici

摘要

We generalise the notions of scalar-valued holomorphic p-contact and s-symplectic structures introduced recently on compact complex manifolds by the second-named author jointly with H. Kasuya and L. Ugarte to their analogues with values in a holomorphic line bundle. We then study the resulting holomorphic p-contact and s-symplectic manifolds which, unlike their scalar counterparts that are never Kähler, can even be projective. In particular, we investigate the (lack of) positivity properties of the canonical bundle of these manifolds when it is given a possibly singular Hermitian fibre metric. One of the tools used is a very recent regularisation result for m-psh functions obtained jointly by S. Dinew and the second-named author.