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 HarbourneHirshowitz 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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