# A Threefold with $p_g=0$ and $P_2=2$

### Ezio Stagnaro

Università di Padova, Italy

## Abstract

We construct a nonsingular threefold *X* with_q_1 = _q_2 = *p__g* = 0 and _P_2 = 2 whose *m*-canonical transformation*φ*|*m__KX*| has the following properties

i) *φ*|*m__KX*| 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.

## Cite this article

Ezio Stagnaro, A Threefold with $p_g=0$ and $P_2=2$. Rend. Sem. Mat. Univ. Padova 121 (2009), pp. 13–31

DOI 10.4171/RSMUP/121-2