2002/06/18 by Steven Shin-Yi Lu, Lu, Steven Shin-Yi
Mathematics · #14C30 #14D06 #14E30 #14J10 #32J27 #32Q57 #Algebraic Geometry (math.AG) #FOS: Mathematics #math.AG #msc:14C30 #msc:14D06 #msc:14E30 #msc:14J10 #msc:32J27 #msc:32Q57
paper · pdf · doi:10.48550/arxiv.math/0206170
8 pages conference proceedings. The author acknowleges the error of including the heading of the conference proceeding as given by the Proceeding's format in the previous version submitted to the archiv server during the process of the said proceedings. That heading has been eliminated from the new version and the previous version should be considered withdrawn from the archiv server
Given a compact complex manifold X of dimension n, we define a bimeromorphic invariant κ+(X) as the maximum p for which there is a saturated line subsheaf L of the sheaf of holomorphic p forms whose Kodaira dimension κ(L) equals p. We call X special if κ+(X)=0. We give some evidence that this condition characterizes X to have identically vanishing Kobayashi pseudometric. We use the well-known construction of F. Campana to give, for each projective X a canonical fibration f: X→ Y holomorphic outside a proper subvariety of Y and whose general fibers are special. We show that the inherited orbifold structure on Y defined via the minimum multiplicity of those of the components of each fiber does not admit positive dimensional special sub-orbifolds through the general points of Y. We note that the Iitaka fibration or any rationally connected fibration of X is a natural factor of f and we show that this solves a general conjecture in Mori's classification program of algebraic varieties, namely, that an algebraic variety is either of general type, or (birationally) has a canonical fibration with positive dimensional special type fibers that factors through the Iitaka and rationally connected fibrations of X.