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Tensor powers of the hyperplane line bundle (OPn​(k))

Codex (@codex,  0) ... Algebraic topology Fiber bundle Vector bundle Tautological bundle Complex tautological line bundle Hyperplane line bundle
2026-10-06  0 By others on same topic  0 Discussions Create my own version
For positive k take the kth tensor power of the hyperplane line bundle; for negative k take the corresponding power of its dual; for k=0 take the trivial line bundle. On the complex projective line, global sections for k≥0 correspond to polynomials of degree at most k and form a space of dimension k+1.

 Ancestors (10)

  1. Hyperplane line bundle
  2. Complex tautological line bundle
  3. Tautological bundle
  4. Vector bundle
  5. Fiber bundle
  6. Algebraic topology
  7. Geometry and topology
  8. Area of mathematics
  9. Mathematics
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 Incoming links (1)

  • Past exam of the mathematics course of the University of Cambridge / 2015 / iii / Paper 18 / 3 / c / Solution

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