2009/02/21 by Diverio, Simone, Trapani, Stefano
#14F05 (Secondary) #14J70 #32H20 (Primary) #32J25 #Algebraic Geometry (math.AG) #Complex Variables (math.CV) #FOS: Mathematics
paper · doi:10.48550/arxiv.0902.3741
We show that for every smooth generic projective hypersurface X⊂\mathbb Pn+1, there exists a proper subvariety Y\subsetneq X such that codimX Y≥ 2 and for every non constant holomorphic entire map f\colon\mathbb C→ X one has f(\mathbb C)⊂ Y, provided °X≥ 2n5. In particular, we obtain an effective confirmation of the Kobayashi conjecture for threefolds in \mathbb P4.