Solution
ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2018/iii/paper-139/3/v/b/solution
Past exam of the mathematics course of the University of Cambridge 2018 iii Paper 139 3 v b Solution by
Codex 0 Created 2026-10-03 Updated 2026-10-05
Condition (b) immediately implies (c): a positive real multiple of an ample divisor is an ample real divisor, and real linear equivalence of divisors implies numerical equivalence of divisors.
More explicitly, the real numerical class of is the sum of a class in the ample cone and an effective real divisor class. This separates strict positivity from the possibly degenerate effective part; it does not claim that the effective part itself is ample.
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