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Deformations of ruled surfaces.

This paper grew out of an investigation of irreducible components of the moduli spaces of surfaces of general type. While studying surfaces with a fibration by curves of genus two which are coverings of ruled surfaces, I found to my surprise that deformations of ruled surfaces over a curve of genus greater than one have never been studied, even though ruled surfaces themselves have been the object of many papers in algebraic geometry during the last hundred years, and the cases of rational ruled surfaces [Hirz] and ruled surfaces over an elliptic curve [Suwa] showed that interesting effects related to the nonexistence of a Hausdorff moduli space do occur.