2010/06/28 by Steven Dale Cutkosky, Cutkosky, Steven Dale
Mathematics · Computer Science · #Algebraic Geometry and Number Theory #Geometric and Algebraic Topology #Polynomial and algebraic computation
paper · pdf · doi:10.48550/arxiv.1006.5369
We give a simpler and more conceptual proof that a morphism from a 3-fold to a surface, over an algebraically closed field of characteristic 0, can be made into a toroidal morphism by sequences of blow ups of nonsingular subvarieties above the domain and range. Our original proof, which is much longer and more complicated, appeared in Springer Lecture Notes in 2002. The final version of this paper is much clearer, thanks to the encouragement of the referee. In particular, Section 5 on global reduction has been completely rewritten. The paper will appear in the Annals of the Fourier Institute.