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 , 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 , such that Z ∩ Sing (X) ≠ ∅. We study the singularities of X through which Z passes.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-bc108-0-7,
author = {M. R. Gonzalez-Dorrego},
title = {Smooth double subvarieties on singular varieties, III},
journal = {Banach Center Publications},
volume = {108},
year = {2016},
pages = {85-93},
zbl = {06622287},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-bc108-0-7}
}
M. R. Gonzalez-Dorrego. Smooth double subvarieties on singular varieties, III. Banach Center Publications, Tome 108 (2016) pp. 85-93. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-bc108-0-7/