The canonical model of a singular curve

被引：23

作者：

Kleiman, Steven Lawrence ^{[1
]}

Martins, Renato Vidal ^{[2
]}

机构：

[1] 2 278 MIT, Dept Math, Cambridge, MA 02139 USA

[2] Univ Fed Minas Gerais, ICEx, Dept Matemat, BR-30123970 Belo Horizonte, MG, Brazil

来源：

GEOMETRIAE DEDICATA | 2009年 / 139卷 / 01期

关键词：

Canonical model; Singular curve; non-Gorenstein curve; GORENSTEIN CURVES; VARIETIES; RINGS;

D O I：

10.1007/s10711-008-9331-4

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We give refined statements and modern proofs of Rosenlicht's results about the canonical model C' of an arbitrary complete integral curve C. Notably, we prove that C and C' are birationally equivalent if and only if C is nonhyperelliptic, and that, if C is nonhyperelliptic, then C' is equal to the blowup of C with respect to the canonical sheaf omega. We also prove some new results: we determine just when C' is rational normal, arithmetically normal, projectively normal, and linearly normal.

引用

页码：139 / 166

页数：28

共 15 条

[1] One-dimensional almost Gorenstein rings [J].