2003/06/03 by Debarre, O. · 3 citations
#14K12 #14M10 #Algebraic Geometry (math.AG) #FOS: Mathematics
paper · doi:10.48550/arxiv.math/0306066
We study smooth projective complex varieties with ample cotangent bundle. Our main result is that in an abelian variety of dimension n, a complete intersection of at least n/2 general hypersurfaces of sufficiently high degrees has ample cotangent bundle. We discuss the conjecture that the analogous statement should hold in the projective space. Finally, we present a construction due to Bogomolov of varieties with ample cotangent bundle as linear sections of a product of varieties with big cotangent bundle.