Surfaces with Many Solitary Points
| dc.creator | Labs, Erwan Brugalle Oliver | |
| dc.date | 2008-01-28 | |
| dc.date | 2008-12-17 | |
| dc.date.accessioned | 2026-07-07T12:13:14Z | |
| dc.date.available | 2026-07-07T12:13:14Z | |
| dc.description | It is classically known that a real cubic surface in the real projective 3-space cannot have more than one solitary point (locally given by x^2+y^2+z^2=0) whereas it can have up to four nodes (x^2+y^2-z^2=0). We show that on any surface of degree at least 3 in the real projective 3-space, the maximum possible number of solitary points is strictly smaller than the maximum possible number of nodes. Conversely, we adapt a construction of Chmutov to obtain surfaces with many solitary points by using a refined version of Brusotti's theorem. Finally, we adapt this construction to get real algebraic surfaces with many singular points of type $A_{2k-1}^\smbullet$ for all $k\ge 1$. | |
| dc.description | 13 pages, 1 figure | |
| dc.identifier | https://arxiv.org/abs/0801.4283 | |
| dc.identifier | http://arxiv.org/abs/0801.4283 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/210775 | |
| dc.subject | Algebraic Geometry | |
| dc.subject | 14J17, 14J70, 14P25 | |
| dc.title | Surfaces with Many Solitary Points | |
| dc.type | text |