by  S.Yu. Orevkov

Abstract:  Main result: let  Y = X - D  where  X  is a smooth projective variety and  D a curve.  Suppose that  Hq(Y,Q) = 0  for  q > 0  and the logarithmic Kodaira dimension of  Y  is  2.  If the boundary of a "tubular neighbourhood" of  D  is a Seifert  Q-homology sphere with  r  multiple fibers then  r < 17.