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On Barth’s conjecture concerining

Published online by Cambridge University Press:  22 January 2016

Mihnea Coltoiu*
Affiliation:
Institute of Mathematics of the Romanian Academy, P.O. Box 1-764, RO-70700 Bucharest, Romania
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A classical, still unsolved problem, is the following: is every connected curve AP3 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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Type
Research Article
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1997

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