Problem Set 4 Jason Starr Fall 2014 MAT 614 Problem Set 4
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چکیده
Problems. Problem 1. Let Y be a finite type, separated k-scheme. Let E be a locally free OY -module of rank r + 1. Let πE : PY (E)→ Y, φ : π∗E∨ → O(1) be a universal pair of a morphism to Y together with an invertible quotient of the pullback of E∨ (to help calibrate conventions, this is covariant in E with respect to locally split monomorphisms of locally free sheaves). Recall in the proof of the splitting principle, for each q = 0, . . . , r and for each integer l ∈ Z, we defined the group homomorphism, π̃∗ q : Al−q(Y )→ Al(PY (E)), βl−q 7→ c1(O(1)) ∩ πβl−q,
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