A Threefold with p(g)=0 and P-2=2

作者：Stagnaro Ezio^*

来源：Rendiconti del Seminario Matematico della Universita di Padova, 2009, 121: 13-31.

DOI：10.4171/rsmup/121-2

We construct a nonsingular threefold X with q(1) = q(2) = p(g) = 0 and P-2 = 2 whose m-canonical transformation phi(vertical bar mKx vertical bar) has the following properties
i) phi(vertical bar mKx vertical bar) has the generic fiber of dimension >= 1, for 2 <= m <= 5;
ii) it is generically a tranformation 2: 1, for 6 <= m <= 8 and m = 10;
iii) it is birational for m = 9 and m >= 11.
So, we have a gap for m = 10 in the birationality of phi(vertical bar mKx vertical bar).

• 出版日期2009