Normal bicanonical and tricanonical threefolds
EZIO STAGNARO

Abstract. The first author to construct a non-normal bicanonical threefold in P⁴ was L. Godeaux in 1936. This threefold has degree 8. In the first part of the present paper, starting from a normal threefold of general type where q₁ = q₂ = p_g = 0, P₂ = P₃ = 5, of degree 6, we construct Godeaux's example and two examples of tricanonical threefolds in P⁴ . One of the tricanonical threefolds is normal. In the second part of the paper, we construct (starting from the beginning) a normal bicanonical threefold of degree 8 that has the birational invariants given by q₁ = q₂ = p_g = 0 and P₂ = 5. No other examples of bicanonical and tricanonical threefolds in P⁴ are known.

Rend. Mat. Appl. (7) 38 (2017) 199-220; pdf