On osculating cones and the Riemann-Kempf singularity theorem for hyperelliptic curves, trigonal curves, and smooth plane quintics
Here we give several examples of projective degenerations of subvarieties of . The more important case considered here is the d-ple Veronese embedding of ; we will show how to degenerate it to the union of n-dimensional linear subspaces of and the union of scrolls. Other cases considered in this paper are essentially projective bundles over important varieties. The key tool for the degenerations is a general method due to Moishezon. We will give elsewhere several applications to postulation...
The classical Segre theory gives a necessary and sufficient condition for a plane curve to be a branch curve of a (generic) projection of a smooth surface in . We generalize this result for smooth surfaces in a projective space of any dimension in the following way: given two plane curves, and , we give a necessary and sufficient condition for to be the branch curve of a surface in and to be the image of the double curve of a -model of . In the classical Segre theory, a plane curve...
Si caratterizzano alcune classi di superfici in relazione all’indice di autointersezione dell'aggiunto ad un divisore molto ampio.
Siano: una superficie algebrica proiettiva complessa non singolare, un divisore canonico ed un divisore molto ampio su . Questo lavoro ha per oggetto lo studio dell'indice di autointersezione . Si dimostra, innanzitutto, la disuguaglianza , nell'ipotesi che la superficie ottenuta immergendo mediante il sistema lineare completo non sia uno scroll. Questa disuguaglianza è connessa con alcuni risultati di Sommese e Van de Ven sulla generazione del fascio . La dimostrazione della (I)...
Some inequalities between the class and the degree of a smooth complex projective manifold are given. Application to the case of low sectional genus are supplied.