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Master's Dissertation
DOI
Document
Author
Full name
Lucas Mioranci
E-mail
Institute/School/College
Knowledge Area
Date of Defense
Published
São Carlos, 2019
Supervisor
Committee
Levcovitz, Daniel (President)
Borges Filho, Herivelto Martins
Tengan, Eduardo
Vainsencher, Israel
Title in Portuguese
Sobre variedades de Veronese defeituosas e o teorema de Alexander-Hirschowitz
Keywords in Portuguese
Geometria algébrica
Sistemas lineares de polinômios homogêneos
Variedades de Veronese
Variedades secantes
Abstract in Portuguese
Este trabalho aborda o problema de determinar todas as variedades de Veronese defeituosas, apresentando uma prova dos casos não-defeituosos. Trabalhamos com a formulação equivalente segundo a qual, a menos de uma pequena lista de exceções, k pontos duplos em Pn impõem condições independentes em polinômios homogêneos de grau d, como demonstrado por J. Alexander e A. Hirschowitz em 1995. Baseamo-nos principalmente no artigo de M. Brambilla e G. Ottaviani, além de adicionar mais detalhes sobre variedades secantes e a relação do teorema com o problema de Waring para polinômios.
Title in English
On defective Veronese varieties and the Alexander-Hirschowitz theorem
Keywords in English
Algebraic geometry
Linear systems of homogeneous polynomials
Secant varieties
Veronese varieties
Abstract in English
This dissertation deals with the problem of determining all defective Veronese varieties by presenting proof of the non-defective cases. We work on the equivalent formulation which says that, except for a small list of exceptions, k double points on Pn impose independent conditions on homogeneous polynomials of degree d, as proved by J. Alexander and A. Hirschowitz in 1995. Our main reference is the paper by M. Brambilla and G. Ottaviani, and we included a few more details on secant varieties and the relation to the Waring problem for polynomials.
 
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Publishing Date
2019-11-19
 
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