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.
Settore MAT/03 - Geometria
dic-2001
Article (author)
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/2434/970243
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