Algebraic geometry II - schemes and sheaves

MATH-510

Content of Lecture 14.11.225

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1) Quasicoherence of the sheaf associated to a graded module.

2) The functor sending a graded module to a sheaf is exact.

3) Serre twists. O(n) is invertible under suitable hypothesis.

4) Nonvanishing locus of a section of an invertible sheaf. Lifting sections from the nonvansihing locus.

5) Under suitable hypothesis, every quasicoherent sheaf on Proj is given by a graded module.