1999/09/29 by K. Oguiso, Oguiso, K., J. Sakurai +1
Mathematics · #14E20 #14J28 #14J32 #14J50 #Algebraic Geometry (math.AG) #FOS: Mathematics #math.AG #msc:14E20 #msc:14J28 #msc:14J32 #msc:14J50
paper · pdf · doi:10.48550/arxiv.math/9909175
38 pages, AMSTeX
arxiv created 1999/09/29 · arxiv updated 2009/11/30
First, we classify Calabi-Yau threefolds with infinite fundamental group by means of their minimal splitting coverings introduced by Beauville, and deduce that the nef cone is a rational simplicial cone and any rational nef divisor is semi-ample if the second Chern class is identically zero. We also derive a sufficient condition for the fundamental group to be finite in terms of the Picard number in an optimal form. Next, we give a concrete structure Theorem concerning c2-contractions of Calabi-Yau threefolds as a generalisation and also a correction of our earlier works for simply connected ones. Finally, as an application, we show the finiteness of the isomorphism classes of c2-contractions of each Calabi-Yau threefold.