When singular points of a reduced scheme are not dense in it? - MathOverflow most recent 30 from http://mathoverflow.net 2013-06-19T01:12:34Z http://mathoverflow.net/feeds/question/21657 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/21657/when-singular-points-of-a-reduced-scheme-are-not-dense-in-it When singular points of a reduced scheme are not dense in it? Mikhail Bondarko 2010-04-17T11:01:18Z 2010-06-01T20:31:07Z <p>A stupid AG question: could singular (Zarisky) points be dense in a reduced (Noetherian) scheme \$S\$? If yes, which 'standard' restrictions on \$S\$ could ensure that this does not happen? For example, should one demand \$S\$ to be excellent? Will anything change if we want singular points not to be dense in any finite type reduced \$S\$-scheme? </p> <p>I would also be gratefull for any ('bad' or 'good') examples.</p> http://mathoverflow.net/questions/21657/when-singular-points-of-a-reduced-scheme-are-not-dense-in-it/26756#26756 Answer by Qing Liu for When singular points of a reduced scheme are not dense in it? Qing Liu 2010-06-01T20:31:07Z 2010-06-01T20:31:07Z <p>For examples with dense singular locus, see William J. Heinzer and Lawrence S. Levy: Domains of Dimension 1 with Infinitely Many Singular Maximal Ideals, Rocky Mountain J. Math. (2007), 203-214. Their examples are affine and noetherian.</p>