Vector Fields on Smooth Threefolds Vanishing on Complete Intersections
Abstract
The existence of a vector field on a compact Kaehler manifold with nonempty zero locus and the properties of this zero locus strongly influence the geometry of the manifold. For example, J. Wahl proved 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 ndimensional 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 3dimensional projective space or the 3dimensional quadric.
 Publication:

arXiv Mathematics eprints
 Pub Date:
 April 2001
 arXiv:
 arXiv:math/0104217
 Bibcode:
 2001math......4217E
 Keywords:

 Algebraic Geometry;
 14M20 (Primary);
 14L99;
 14F05 (Secondary)
 EPrint:
 11 pages