A threefold of general type with \(q_1 = q_2 = p_g = P_2 = 0\)
The author contructs a smooth projective complex threefold of general type \(X\) such that \(h^i({\mathcal O}_X)=0\) for \(i>0\) and \(h^0(K_X)=h^0(2K_X)=0\). This is in contrast with the case of surfaces, since for a surface of general type \(S\) one always has \(h^0(2K_S)>0\). In the paper it is also shown that the \(m\)-canonical map of the example constructed is birational if and only if \(m\geq 14\). The example arises as a desingularization of a hypersurface of degree 10 in \(4\)-dimensional projective space.
scientific article; zbMATH DE number 1901296