A new construction of a compactification of ${\bf C}^3$

Abstract

Let (X, Y) be a smooth projective compactification of C 3 , namely, Xis a smooth projective 3-fold and Fis a subvariety of X such that X-Fis analytically isomorphic to C 3 . We will write simply as X-Y^ C 3 if there is an algebraic isomorphism of X-Y onto C 3 . Assume that Yis normal. Then A^is a Fano 3-fold of index r(\ <r<4) with the second Betti number b 2 (X) = 1, and Y is a hyperplane section of X. Then, in the paper [1], we have the following results: