Abstract
A classical, still unsolved problem, is the following: is every connected curve A ⊂ P3 a set-theoretic complete intersection? It is clear that if A is a set-theoretic complete intersection then:a) The algebraic cohomology groups vanish for every coherent algebraic sheaf on P3.b) The analytic cohomology groups vanish for every coherent analytic sheaf on P3\A.
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