Adeegso tilmaantan si aad u carrabbaabdo ama ugu samayso link qoraalkan
http://hdl.handle.net/2307/602
Cinwaan: | Degenerations and applications : polynomial interpolation and secant degree | Qore: | Postinghel, Elisa | Tifaftire: | Ciliberto, Ciro | Taariikhda qoraalka: | 7-Apr-2010 | Tifaftire: | Università degli studi Roma Tre | Abstract: | The polynomial interpolation problem in several variables and higher multiplicities is a subject that has been widely studied, but there is only a little understanding about the question. What is known, so far, is essentially concentrated in the Alexander-Hirschowitz Theorem which says that a general collection of double points in Pr gives independent conditions on the linear system L of the hypersurfaces of degree d, with a well known list of exceptions. In the first part of this thesis we present a new proof of this theorem which consists in performing degenerations of Pr and analyzing how L degenerates. Our construction gives hope for further extensions to greater multiplicities. There is a long tradition within algebraic geometry that studies the dimension and the degree of k -secant varieties. These are problems that are unsolved in general. In the second part of the thesis, we consider any projective toric surface XP associated to a polytope P ⊆ R2 and we perform planar toric degenerations D of XP in order to study the k -secant varieties of XP . In particular we give a lower bound to the secant degree and to the 2-secant degree of XP , taking into account the singularities of the configuration D of non-delightful planar toric degenerations. 1 | URI : | http://hdl.handle.net/2307/602 |
Wuxuu ka dhex muuqdaa ururinnada: | Dipartimento di Matematica e Fisica T - Tesi di dottorato |
Fayl ku dhex jira qoraalkan:
Fayl | Sifayn | Baac | Fayl | |
---|---|---|---|---|
degenerations_and_applications_polynomial_interpolation_and_.pdf | 675.34 kB | Adobe PDF | Muuji/fur |
Page view(s)
129
Last Week
0
0
Last month
1
1
checked on Nov 22, 2024
Download(s)
27
checked on Nov 22, 2024
Google ScholarTM
Check
Dhammaan qoraallada lagu kaydiyay DSpace waxay u dhowrsanyihiin xuquuqda qoraha.