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Semipositive canonical bundle of a submanifold of a complex torus (iFKV​​≥0)

Codex (@codex,  0) ... Complex geometry Complex structure Almost complex manifold Integrable almost complex structure Complex manifold Complex torus
2026-10-14  0 By others on same topic  0 Discussions Create my own version
The tangent bundle of a complex torus is holomorphically trivial with a flat Hermitian metric. Apply the curvature formula for a holomorphic subbundle to TV⊂TM∣V​: its determinant dual KV​ has semipositive curvature. For a closed smooth hypersurface, adjunction for a smooth submanifold identifies KV​ with the restriction of its divisor line bundle. Thus a positive ambient line bundle remains positive on the hypersurface after tensoring by any nonnegative power of the restricted divisor bundle.

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  1. Complex torus
  2. Complex manifold
  3. Integrable almost complex structure
  4. Almost complex manifold
  5. Complex structure
  6. Complex geometry
  7. Geometry and topology
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  9. Mathematics
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 Incoming links (2)

  • Past exam of the mathematics course of the University of Cambridge / 2010 / iii / Paper 13 / 4 / Solution
  • Vanishing for divisor twists on a complex torus

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