Le Matematiche (Dipartimento di Matematica e Informatica, Università degli Studi di Catania)
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Sobolev\u27s original definition of his spaces revisited and a comparison with nowadays definition
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Graded Betti numbers of general finite subsets of points on projective varieties
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Un problema di Darboux in un insieme non limitato. Esistenza, unicità e dipendenza continua della soluzione
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On the singularities of the trisecant surface to a space curve
Get PDFLet C be a smooth curve in P^3 . Trisecant lines to the curve C are, in general, sweeping out a (reduced) surface in P^3 . In this note we attempt to describe some of its singularities, and in particular we show that if the curve C has only a finite number of quadrisecant lines, then the singular locus contains the quadrisecant lines to C, and the points through which pass more trisecants than through a generic point of the trisecant surface. Several explicit examples are discussed in the last section
Minimal models and the virtual degree of Seifert fibered spaces
Get PDFWe compute the minimal models (in the sense of Sullivan) of Seifert fibered spaces and show that they are classified by the virtual degree. As a consequence, we reobtain the results of Neumann-Raymond (1978) on the virtual degree of Seifert fibered spaces
Semilinear equations on nilpotent Lie groups: global existence and blow-up of solutions
Get PDFIn this note we consider a semilinear Cauchy problem on a nilpotent Lie group. We extend a classical result by Fujita about the global existence and the blow-up of solutions