Given a smooth k-variety Y (where k is a field of arbitrary characteristic) and a linear systemL on Y we study the dimension of the singular locus of the general element ofL, both inside and outside the base locus B ofL. We interpret these results from the point of view of the transversality theory, and we improve a result by Speiser about the not too ramified morphisms. Moreover, we show that our results can be applied in some cases where a criterion by Zhang, for the smoothness of the general element ofL, fails.
Linear systems, singularity and not too ramified morphisms / M.L. Spreafico. - In: ANNALI DI MATEMATICA PURA ED APPLICATA. - ISSN 0373-3114. - 179:1(2001 Dec), pp. 295-307. [10.1007/BF02505960]
Linear systems, singularity and not too ramified morphisms
M.L. Spreafico
2001
Abstract
Given a smooth k-variety Y (where k is a field of arbitrary characteristic) and a linear systemL on Y we study the dimension of the singular locus of the general element ofL, both inside and outside the base locus B ofL. We interpret these results from the point of view of the transversality theory, and we improve a result by Speiser about the not too ramified morphisms. Moreover, we show that our results can be applied in some cases where a criterion by Zhang, for the smoothness of the general element ofL, fails.
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