A globally generated line bundle on a quasi-compact scheme is generated by finitely many global sections. Each point has a section generating on an open neighbourhood, and quasi-compactness gives a finite subcover. This supplies a map into a fixed finite-dimensional projective space associated with that line bundle.

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  1. Globally generated line bundle
  2. Line bundle
  3. Locally free sheaf
  4. Sheaf of modules
  5. Ringed space
  6. Algebraic geometry
  7. Geometry and topology
  8. Area of mathematics
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