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Legendrian varieties and quasi-ordinary hypersurfaces
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Orientador(es)
Resumo(s)
This thesis is a study of the Legendrian Varieties that are conormals of
quasi-ordinary hypersurfaces.
In the first chapter we study the analytic classification of the Legendrian
curves that are the conormal of a plane curve with a single Puiseux pair.
Let m,n be the set of Legendrian curves that are the conormal of a plane
curve with a Puiseux pair (m, n), where g.c.d.(m, n) = 1 and m > 2n, with
semigroup as generic as possible. We show that the quotient of m,n by
the group of contact transformations is a Zariski open set of a weighted
projective space.
The main tool used in the proof of this theorem is a classification/construction
theorem for contact transformation that has since proved useful in other instances.
In the second chapter we calculate the limits of tangents of a quasi-ordinary
hypersurface. In particular, we show that the set of limits of tangents is, in
general, a topological invariant of the hypersurface.
In the third chapter we prove a desingularization theorem for Legendrian
hypersurfaces that are the conormal of a quasi-ordinary hypersurface. One
of the main ingredients of the proof is the calculation of the limits of tangents
achieved in chapter two.
Descrição
Tese de doutoramento, Matemática (Geometria e Topologia), Universidade de Lisboa, Faculdade de Ciências, 2011
Palavras-chave
Espacos de moduli Geometria algébrica Limites (Matemática) Variedades (Matemática) Teses de doutoramento - 2011