Global smoothings of degenerate Del Pezzo surfaces with normal crossings

摘要

Fujita classified one-parameter degenerations of Del Pezzo manifolds with smooth total spaces, which includes the complete classification of semi-stable degenerations of Del Pezzo surfaces. We prove the converse, namely, for a given semi-stable Del Pezzo surface of each type in the list of Fujita, there exists a smoothing of it with a smooth total space.