The irregularity of the direct image of some \({\mathcal D}\)-modules (Q998131)

Let \(U\) be a smooth affine complex variety and \(f,g:U \to\mathbb C\) two regular functions. Let \(M\) be a regular holonomic \(D_U\)-module. The author studies the irregularity of the direct image complex \(f_+(Me^g)\) on the line \(\mathbb C\) and relates it to the characteristic cycles of the systems \(H^k(f,g)_+(M)\) on the plane \(\mathbb C^2\).