1998/06/26 by S. Di Rocco, Di Rocco, S., A. J. Sommese +1 · 1 citation
Mathematics · #14J40 #14M99 #Algebraic Geometry (math.AG) #FOS: Mathematics #math.AG #msc:14J40 #msc:14M99
paper · pdf · doi:10.48550/arxiv.math/9806144
Latex file, 5 pages
arxiv created 1998/06/26 · arxiv updated 2009/11/30
We characterize the triples (X,L,H), consisting of holomorphic line bundles L and H on a complex projective manifold X, such that for some positive integer k, the k-th holomorphic jet bundle of L, Jk(L), is isomorphic to a direct sum H+...+H. Given the geometrical constrains imposed by a projectivized line bundle being a product of the base and a projective space it is natural to expect that this would happen only under very rare circumstances. It is shown, in fact, that X is either an Abelian variety or projective space. In the former case L≅ H is any line bundle of Chern class zero. In the later case for k a positive integer, L=OPn(q) with Jk(L)=H+...+H if and only if H=OPn(q-k) and either q≥ k or q≤ -1.