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2 results

  • Numerical dimension and a Kawamata–Viehweg–Nadel-type vanishing theorem on compact Kähler manifolds

  • Part of
  • Junyan Cao
  • Journal:
    Compositio Mathematica / Volume 150 / Issue 11 / November 2014
    Published online by Cambridge University Press:
    27 August 2014, pp. 1869-1902
    Print publication:
    November 2014
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  • Let $X$ be a compact Kähler manifold and let $(L,{\it\varphi})$ be a pseudo-effective line bundle on $X$. We first define a notion of numerical dimension for pseudo-effective line bundles with singular metrics, and then discuss the properties of this numerical dimension. Finally, we prove a very general Kawamata–Viehweg–Nadel-type vanishing theorem on an arbitrary compact Kähler manifold.

  • Complex submanifolds, connections and asymptotics

  • Part of
  • Tatyana Foth
  • Journal:
    Proceedings of the Edinburgh Mathematical Society / Volume 53 / Issue 2 / June 2010
    Published online by Cambridge University Press:
    30 April 2010, pp. 373-383
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  • Let L → X be a positive line bundle on a compact complex manifold X. For compact submanifolds Y, S of X and a holomorphic submersion Y → S with compact fibre, we study curvature of a natural connection on certain line bundles on S.