Divisibility of ideals and blowing up

Moody, John Atwell

Illinois J. Math., Tome 45 (2001) no. 4, p. 163-165 / Harvested from Project Euclid

Résumé

Let $R$ be a Noetherian integral domain, let $V=\Spec(R)$, and let $I, J$ be nonzero ideals of $R$. Clearly, if $J$ is either a divisor of $I$ or a power of $I$ there is a map $Bl_I(V)\to Bl_J(V)$ of schemes over $V.$ The purpose of this note is to prove, conversely, that if such a map exists, then $J$ must be a fractional ideal divisor of some power of $I$.

Publié le : 2001-01-15
Classification: 14E05, 13A30

@article{1258138260,
     author = {Moody, John Atwell},
     title = {Divisibility of ideals and blowing up},
     journal = {Illinois J. Math.},
     volume = {45},
     number = {4},
     year = {2001},
     pages = { 163-165},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1258138260}
}

Moody, John Atwell. Divisibility of ideals and blowing up. Illinois J. Math., Tome 45 (2001) no. 4, pp.  163-165. http://gdmltest.u-ga.fr/item/1258138260/