On irregular threefolds and fourfolds with numerically trivial canonical bundle (Q329963)

The author studies smooth irregular 3-folds and 4-folds with numerical trivial canonical class so that \(K_X\equiv 0\) and \(h^1(\mathcal O _X)>0\). He shows that if \(\dim X=3\) and \(L\) is a nef and big divisor, then \(|mL+P|\) defines a birational map for \(m\geq 3\) and any topologically trivial line bundle \(P\in \text{Pic}^0(X)\). If \(\dim X=4\) and \(L\) is an ample divisor, then \(|mL+P|\) defines a birational map for \(m\geq 5\) and any \(P\in \text{Pic}^0(X)\). Both of these results are optimal.