Remarks on the postulation of zero-dimensional subschemes of projective space.
Sull’integrità e la fattorialità dei completamenti -adici
Seminormalità delle varietà di Gorenstein
We characterize those Gorenstein algebraic varieties which are seminormal (in the sense of [11]), by describing their singularities in codimension 1. In particular a plane curve is seminormal if, and only if, it has at most ordinary double points (as proved by P. Salmon in [10]); and a surface in 3-space is seminormal if, and only if, it has at most "biplanar" double curves. It follows that a surface with "ordinary singularities" only is seminormal, as proved by E. Bombieri in [5].
Sulla nozione di preschema henseliano
In this Note we state the bases of a theory of henselian preschemes, similar to the theory of formal preschemes. The definition of affine henselian scheme (and hence of henselian prescheme) is quite natural, but becomes meaningful only after proving a suitable sheaf axiom (§ 2), which can be generalized to sheaves associated with modules (§ 3). A brief discussion of henselization of a prescheme along a closed subprescheme concludes the paper (§ 4).
Gap orders of rational functions on plane curves with few singular points.
Theorems and for henselian schemes
Schema di una dimostrazione dei Teoremi e per fasci quasi coerenti su uno schema henseliano affine.
Bertini theorems for weak normality
Nagata's Criterion and Openness of Loci for Gorenstein and Complete Intersection.
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