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Smooth double subvarieties on singular varieties, III

100%

Gonzalez-Dorrego M.

Banach Center Publications

2016

tom 108

nr 1

85-93

Let k be an algebraically closed field, char k = 0. Let C be an irreducible nonsingular curve such that rC = S ∩ F, r ∈ ℕ, where S and F are two surfaces and all the singularities of F are of the form $z³ = x^{3s} - y^{3s}$, s ∈ ℕ. We prove that C can never pass through such kind of singularities of a surface, unless r = 3a, a ∈ ℕ. We study multiplicity-r structures on varieties r ∈ ℕ. Let Z be a reduced irreducible nonsingular (n-1)-dimensional variety such that rZ = X ∩ F, where X is a normal n-fold, F is a (N-1)-fold in $ℙ^{N}$, such that Z ∩ Sing (X) ≠ ∅. We study the singularities of X through which Z passes.

On triple curves through a rational triple point of a surface

100%

Gonzalez-Dorrego M.

Annales Polonici Mathematici

2006

tom 88

nr 1

1-17

Let k be an algebraically closed field of characteristic 0. Let C be an irreducible nonsingular curve in ℙⁿ such that 3C = S ∩ F, where S is a hypersurface and F is a surface in ℙⁿ and F has rational triple points. We classify the rational triple points through which such a curve C can pass (Theorem 1.8), and give an example (1.12). We only consider reduced and irreducible surfaces.

Ograniczanie wyników

1 Annales Polonici Mathematici

1 Banach Center Publications

2 Gonzalez-Dorrego M.

1 2016

1 2006

Wyniki wyszukiwania

Smooth double subvarieties on singular varieties, III

On triple curves through a rational triple point of a surface