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Some questions in algebraic geometry (vector bundles, normal bundles and fat points)

Chiodera, Ludovica (2012) Some questions in algebraic geometry (vector bundles, normal bundles and fat points). PhD Thesis , Università degli studi di Ferrara.

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    Abstract

    In this paper we deal with three argument. In the first part we study rank two globally generated vector bundles on P^n. We classify this bundles through their Chern class, until c_1 = 5 (where c_1 indicates first Chern class). In the second part we deal with normal bundle of projective normal curves. More precisely there is a conjecture, due to Hartshorne and we prove it for some particular case. In the end we study subschemes of P² with fat points. In particulary given Z subscheme of P², we want to understand if Z has maximum rank. We analyze the cases with ten fat points of multiplicity almost eight. To sole this problem, we present a proof of Harbourne-Hirshowitz conjecture for linear system with multiple points of order eight or less and then we prove that every analyzed case has maximum rank.

    Item Type:Thesis (PhD Thesis)
    Date:8 March 2012
    Tutor:Ellia, Philippe
    Coordinator:Ruggiero, Valeria
    Institution:Università degli studi di Ferrara
    PhD:XXIV Anno 2009 > MATEMATICA E INFORMATICA
    Divisions:Dipartimento > Matematica
    Subjects:Area 01 - Scienze matematiche e informatiche > MAT/03 Geometria
    Uncontrolled Keywords:fibrati vettoriali, fibrato normale, punti grassi, vector bundles, normal bundles, fat points
    Deposited on:21 Feb 2013 13:30

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