2010/10/07 by Dmitri Panov, Panov, Dmitri
Mathematics · #Algebraic Geometry (math.AG) #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Topology (math.GT) #math.AG #math.DG #math.GT
paper · pdf · doi:10.48550/arxiv.1010.1448
Revised version accepted in GAFA
arxiv created 2011/07/11 · arxiv updated 2011/07/12
We study complex surfaces with locally CAT(0) polyhedral Kahler metrics and construct such metrics on CP2 with various orbifold structures. In particular, in relation to questions of Gromov and Davis-Moussong we construct such metrics on a compact quotient of the two-dimensional unite complex ball. In the course of the proof of these results we give criteria for Sasakian 3-manifolds to be globally CAT(1). We show further that for certain Kummer coverings of CP2 of sufficiently high degree their desingularizations are of type K(pi,1).