Vector fields on smooth threefolds vanishing on complete intersections |
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Authors: | Thomas Eckl |
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Institution: | Institut für Mathematik, Universit?t Bayreuth, Universit?tsstrasse 30,?95440 Bayreuth, Germany. e-mail: thomas.eckl@uni-bayreuth.de, DE
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Abstract: | A result of J. Wahl shows that the existence of a vector field vanishing on an ample divisor of a projective normal variety
X implies that X is a cone over this divisor. If X is smooth, X will be isomorphic to the n-dimensional projective space.
This paper is a first attempt to generalize Wahl's theorem to higher codimensions: Given a complex smooth projective threefold
X and a vector field on X vanishing on an irreducible and reduced curve which is the scheme theoretic intersection of two
ample divisors, X is isomorphic to the 3-dimensional projective space or the 3-dimensional quadric.
Received: 24 April 2001 |
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Keywords: | Mathematics Subject Classification (2000): Primary 14M20 Secondary 14L99 14F05 |
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