Multiple Structures on Smooth on Singular Varieties

M. R. Gonzalez-Dorrego ()
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M. R. Gonzalez-Dorrego: Universidad Autónoma de Madrid, Departamento de Matemáticas

A chapter in Singularities, Algebraic Geometry, Commutative Algebra, and Related Topics, 2018, pp 383-389 from Springer

Abstract: Abstract Let k an algebraically closed field, char k = 0. Let C be an irreducible nonsingular curve such that rC = S ∩ F, r ∈ ℕ $$r\in \mathbb {N}$$ , where S and F are two surfaces in ℙ 3 $$\mathbb {P}^3$$ and all the singularities of F are of the form z p = x ps − y ps, p prime, s ∈ ℕ $$s\in \mathbb {N} $$ . We prove that C can never pass through such kind of singularities of a surface, unless r = pa, a ∈ ℕ $$a\in \mathbb {N}$$ . These singularities are Kodaira singularities.

Keywords: 14B05; 14E15; 32S25; 14J17; 14J30; 14J35; 14J40; 14J70 (search for similar items in EconPapers)
Date: 2018
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-319-96827-8_15

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DOI: 10.1007/978-3-319-96827-8_15

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