Algebraic geometry II - schemes and sheaves

MATH-510

Lecture 27 (18.12.24) Summary

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1) Cohomology of invertible sheaves on projective spaces.

2) On a projective scheme, the chomology groups of a cohorent sheaf is finitely generated.

3) High enough twist of a coherent sheaf by an ample sheaf on a projective scheme does not have any higher cohomology.