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Jul 7, 2010 at 0:10 comment added Charles Staats I believe (although I cannot immediately bring to mind a proof) that such a projective bundle is again a projective scheme, but I don't know about a quick way of obtaining explicit equations for it. How exactly are your section sheaves given? Do you have a graded module over the coordinate ring, or modules over certain open affines with glueing rules? How are these modules specified?
Jul 6, 2010 at 22:30 history asked Jad CC BY-SA 2.5