McKay correspondence for the Poincare series of Kleinian and Fuchsian singularities

被引：10

作者：

Ebeling, Wolfgang ^{[1
]}

Ploog, David ^{[1
]}

机构：

[1] Leibniz Univ Hannover, Inst Algebra Geometrie, D-30060 Hannover, Germany

来源：

MATHEMATISCHE ANNALEN | 2010年 / 347卷 / 03期

关键词：

NORMAL SURFACE SINGULARITIES; WILD CANONICAL ALGEBRAS; C-STAR-ACTION; AUTOMORPHIC-FORMS;

D O I：

10.1007/s00208-009-0451-4

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We give a uniform and, to a large extent, geometrical proof that the Poincare series of the coordinate algebra of a Kleinian singularity and of a Fuchsian singularity of genus 0 is the quotient of the characteristic polynomials of two Coxeter elements. These Coxeter elements are interpreted geometrically, using 2-Calabi-Yau triangulated categories and spherical twist functors.

引用

页码：689 / 702

页数：14

共 22 条

[1]

[Anonymous], 2006, OXFORD MATH MONOGR

[2]

Dolgachev I.V., 1975, FUNCT ANAL APPL, V9, p[149, 67]

[3]

Dolgachev IV, 2009, CRM PROC & LECT NOTE, V47, P111

[4] ON THE LINK SPACE OF A GORENSTEIN QUASIHOMOGENEOUS SURFACE SINGULARITY [J].

DOLGACHEV, IV .

MATHEMATISCHE ANNALEN, 1983, 265 (04) :529-540

[5]

DOLGACHEV IV, AUTOMORPHIC FORMS WE

[6] Tame and wild projective curves and classification of vector bundles [J].

Drozd, YA ;

Greuel, GM .

JOURNAL OF ALGEBRA, 2001, 246 (01) :1-54

[7] The Poincare series of some special quasihomogeneous surface singularities [J].

Ebeling, W .

PUBLICATIONS OF THE RESEARCH INSTITUTE FOR MATHEMATICAL SCIENCES, 2003, 39 (02) :393-413

[8] Poincare series and monodromy of a two-dimensional quasihomogeneous hypersurface singularity [J].

Ebeling, W .

MANUSCRIPTA MATHEMATICA, 2002, 107 (03) :271-282

[9]

GONZALEZSPRINBERG G, 1983, ANN SCI ECOLE NORM S, V16, P409

[10] McKay correspondence and Hilbert schemes in dimension three [J].

Ito, Y ;

Nakajima, H .

TOPOLOGY, 2000, 39 (06) :1155-1191

← 1 2 3 →