Linear systems, singularity and not too ramified morphisms (Q1409664)

The paper is devoted to questions related to transversality theory. A bound is given for the dimension of the singular locus of the general element of a linear system \(\mathcal L\) inside and outside the base locus \(B\) of \(\mathcal L\). The method is algorithmic and can be implemented into a computer algebra system. Examples shows that the bound is sharp. A result of Speiser about the ``not too ramified'' morphisms is improved. Remark 3.4 shows the applicability of this paper to certain cases where a criterion of Zhang for the smoothness of the general element of \(\mathcal L\) is not usable.