Bounds for the number of moduli for irregular varieties of general type (Q1112125)

Let \(M_ X\) denote the dimension of the set of equivalence classes of complex structures on the differential manifold underlying a minimal surface X of general type. If the irregularity q(X)\(\geq 3\) and there are \(\omega,\omega '\in H^ 0(\Omega^ 1_ X)\) such that \(C=(\omega \wedge \omega '=0)\) is reduced and irreducible, the author proves Castelnuovo's bound \(M_ X\leq P_ g(X)+2q(X).\) The starting point is the inequality \(M_ X\leq h^ 1(\theta_ X)\), from Kodaira-Spencer-Kuranishi theory. The work is motivated by similar results of Catanese. The above result is extended to higher dimensions. The paper is well laid out, but with a few technical imperfections.