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Titolo/Abstract/Parole chiave

Equivalent birational embeddings.

Polastri, Elena (2009) Equivalent birational embeddings. Tesi di Dottorato , Università degli studi di Ferrara.

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    Abstract

    Let X be a projective variety of dimension r. We want to understand when two birational embeddings of the same variety are equivalent up to a Cremona transformation of the projective space, in this case we say that they are Cremona equivalent. It is proven that two birational embeddings of X in Pn with n >= r + 2 are Cremona equivalent. To do this, it is produced a chain of Cremona transformations that modify the linear systems giving the two embeddings one into the other. This is done by looking at the two birational embeddings as different projections of a common embedding. On the other hand, if n = r + 1, there are birationally divisors that are not Cremona equivalent. The case of plane curves is studied in details. Let C be an irreducible and reduced plane curve of arbitrary genus. It is proven that the curve C is birational to either a line; either a curve C, where the log pair (P2,3/dC)has canonical singularities, the log canonical divisor nef and Kodaira dimension k = 0; or a curve C ~ aC0 + bf Fa, where the log pair (Fa,2/aC) has canonical singularities and terminal singularities in a neighborhood of the exceptional curve C0 Fa, the log canonical divisor nef and Kodaira dimension k <= 1. Finally, it is used the theory of &–minimal models to under- stand whether a rational, irreducible and reduced curve is Cremona equivalent to a line.

    Tipologia del documento:Tesi di Dottorato (Tesi di Dottorato)
    Data:17 Marzo 2009
    Relatore:Mella, Massimiliano
    Coordinatore ciclo:Zanghirati, Luisa
    Istituzione:Università degli studi di Ferrara
    Dottorato:XXI Anno 2006 > MATEMATICA E INFORMATICA
    Struttura:Dipartimento > Matematica
    Soggetti:Area 01 - Scienze matematiche e informatiche > MAT/03 Geometria
    Parole chiave:birational embeddings, birational map, Cremona equivalence, plane curves
    Depositato il:03 Lug 2009 14:31

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