A Threefold of General Type with q1=q2=pg=P2=0

Abstract

One of the problems in classifying nonsingular threefolds of general type with pg=0 lies in finding the range of the bigenus P2 (surfaces of general type with pg=0 have 2≤P2≤10). Another problem involves finding the minimum integer m such that the m-canonical map Φ|mK| is birational for any threefold (m=5 in the case of surfaces). An example of a nonsingular threefold X of general type with q1=q2=0, pg=P2=0,P3=1 is presented. In addition, the m-canonical map of X is birational if and only if m≥14. The threefold is obtained as a nonsingular model of a degree ten hypersurface in P4C with the affine equation t2=f10(x,y,z).