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On projective degenerations of Veronese spaces

Edoardo Ballico (1996)

Banach Center Publications

Here we give several examples of projective degenerations of subvarieties of t . The more important case considered here is the d-ple Veronese embedding of n ; we will show how to degenerate it to the union of d n n-dimensional linear subspaces of t ; t : = ( n + d ) / ( n ! d ! ) - 1 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...

On ramified covers of the projective plane II: Generalizing Segre’s theory

Michael Friedman, Rebecca Lehman, Maxim Leyenson, Mina Teicher (2012)

Journal of the European Mathematical Society

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 3 . We generalize this result for smooth surfaces in a projective space of any dimension in the following way: given two plane curves, B and E , we give a necessary and sufficient condition for B to be the branch curve of a surface X in N and E to be the image of the double curve of a 3 -model of X . In the classical Segre theory, a plane curve...

On the adjoint system to a very ample divisor on a surface and connected inequalities

Antonio Lanteri, Marino Palleschi (1981)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

Siano: S una superficie algebrica proiettiva complessa non singolare, K un divisore canonico ed H un divisore molto ampio su S . Questo lavoro ha per oggetto lo studio dell'indice di autointersezione ( K + H ) 2 . Si dimostra, innanzitutto, la disuguaglianza ( K + H ) 2 0 , nell'ipotesi che la superficie S ottenuta immergendo S mediante il sistema lineare completo | H | non sia uno scroll. Questa disuguaglianza è connessa con alcuni risultati di Sommese e Van de Ven sulla generazione del fascio 𝒪 s ( K + H ) . La dimostrazione della (I)...

On the class of some projective varieties.

Edoardo Ballico, Marina Bertolini, Cristina Turrini (1997)

Collectanea Mathematica

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.

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