ON THE SINGULARITIES OF SURFACES RULED BY CONICS

被引：1

作者：

Brundu, Michela ^{[1
]}

Sacchiero, Gianni ^{[1
]}

机构：

[1] Univ Trieste, Dipartimento Matemat & Geosci, I-34127 Trieste, Italy

来源：

COMMUNICATIONS IN ALGEBRA | 2014年 / 42卷 / 05期

关键词：

Conic bundle; Projective surface; Rational singularities; Ruled surface;

D O I：

10.1080/00927872.2012.749884

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We classify the singularities of a surface ruled by conics: they are rational double points of type A(n) or D-n. This is proved by showing that they arise from a precise series of blow-ups of a suitable surface geometrically ruled by conics. We determine also the family of such surfaces which are birational models of a given surface ruled by conics and obtained in a minimal way from it.

引用

页码：1857 / 1879

页数：23

共 50 条

[1] On rational surfaces ruled by conics
Brundu, M
Sacchiero, G
COMMUNICATIONS IN ALGEBRA, 2003, 31 (08) : 3631 - 3652
[2] On the computation of singularities of parametrized ruled surfaces
Perez-Diaz, Sonia
Blasco, Angel
ADVANCES IN APPLIED MATHEMATICS, 2019, 110 : 270 - 298
[3] Algebraic ruled surfaces and their singularities.
Gambier, B
COMPTES RENDUS HEBDOMADAIRES DES SEANCES DE L ACADEMIE DES SCIENCES, 1932, 195 : 745 - 747
[4] A removable singularities theorem for families of ruled surfaces
Harris, A
MATHEMATISCHE ZEITSCHRIFT, 1996, 222 (03) : 479 - 493
[5] Topology of simple singularities of ruled surfaces in Rp
Barbosa, Grazielle Feliciani
Martins, Rodrigo
Saia, Marcelo Jose
TOPOLOGY AND ITS APPLICATIONS, 2012, 159 (02) : 397 - 404
[6] GEOMETRIC ALGEBRA AND SINGULARITIES OF RULED AND DEVELOPABLE SURFACES
Tanaka, Junki
Ohmoto, Toru
JOURNAL OF SINGULARITIES, 2020, 21 : 249 - 267
[7] Singularities of ruled surfaces in R3
Izumiya, S
Takeuchi, N
MATHEMATICAL PROCEEDINGS OF THE CAMBRIDGE PHILOSOPHICAL SOCIETY, 2001, 130 : 1 - 11
[8] DERIVATIONS WITH ONLY DIVISORIAL SINGULARITIES ON RATIONAL AND RULED SURFACES
GANONG, R
RUSSELL, P
JOURNAL OF PURE AND APPLIED ALGEBRA, 1982, 26 (02) : 165 - 182
[9] Finitely determined singularities of ruled surfaces in R3
Martins, R.
Nuno-Ballesteros, J. J.
MATHEMATICAL PROCEEDINGS OF THE CAMBRIDGE PHILOSOPHICAL SOCIETY, 2009, 147 : 701 - 733
[10] A ruled residue theorem for function fields of conics
Gupta, Parul
Becher, Karim Johannes
JOURNAL OF PURE AND APPLIED ALGEBRA, 2021, 225 (06)

← 1 2 3 4 5 →