Abstract.
Let k be a field of any characteristic and not necessarily algebraically closed. In this paper we extend some results of the transversality theory to larger families of k-schemes and of k-morphisms and to all the local geometric properties satisfying some given axioms (for example: geom. regular, geom. reduced, geom. normal and the properties S r and R s ). As an application, we obtain a generalization of the well known Bertini type theorems for local geometric axiomatic properties.
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Received: 2.8.1995
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Luisa Spreafico, M. Axiomatic theory for transversality and Bertini type theorems. Arch. Math. 70, 407–424 (1998). https://doi.org/10.1007/s000130050213
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DOI: https://doi.org/10.1007/s000130050213