## Recent results on holomorphic vector fields: lecture delivered at the Regional Conference on Differential Geometry at Michigan State University, June 15-19, 1970 |

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1-form of type 1-parameter abelian group abelian variety Albanese variety anti holomorphic 1-form anti-holomorphic AutQ bundle automorphism bundle F Chern class Chern form cohomology class common fixed point compact Kahler manifold complex forms complex line bundle complex manifold complex torus complex vector field complex vector space covariant 2-tensor field curvature form define differential form dimc dimension exact sequence exists exp 27ri field of type following theorem harmonic form hence Hermitian form Hermitian metric Hodge manifold Hodge metric holomorphic functions holomorphic vector field Hq(X identify isomorphism Jacobi homomorphism Jacobi map Kahler metric kernel l-parameter subgroup Let F Lie algebra Lie derivative log f metric g non-vanishing Picard variety PN(C projective imbedding Proof Proposition real 2-form real vector field resp sheaf smooth function subalgebra symmetric covariant 2-tensor tensor torus type p,q vector bundle volume element zero(X