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SOLVED:Prove that every one-dimensional proper scheme X over an algebraically closed field k is projective (a) If X is irreducible and nonsingular, then X is projective by (II, 6.7 ) (b) If X is integral, let X̃ be its normalization (II, Ex. 3.8). Show that X̃ is complete and nonsingular, hence projective by (a). Let f: X̃ →X be the projection. Let 𝒬 be a very ample invertible sheaf on X̃. Show there is an effective divisor D=∑Pi on X̃ with ℒ(D) ≅ℒ, and such that f(Pi) is a nonsingular point of

SOLVED:Prove that every one-dimensional proper scheme X over an algebraically closed field k is projective (a) If X is irreducible and nonsingular, then X is projective by (II, 6.7 )

Prove that every one-dimensional proper scheme X over an algebraically closed field k is projective (a) If X is irreducible and nonsingular, then X is projective by (II, 6.7 ) (b) If X is integral, let X̃ be its normalization (II, Ex. 3.8). Show that X̃ is complete and nonsingular, hence projective by (a). Let f: X̃ →X be the projection ...

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عاجل: الصحفي والاعلامي الشجاع قصي شفيق يعلن خبر توقيف مستشار رئيس الوزراء عبد الكريم الفيصل وحبسه 30 يوماً على ذمة

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