McKay correspondence for the Poincar¨¦ series of Kleinian and Fuchsian singularities

详细信息    查看全文

• 作者：Wolfgang Ebeling and David Ploog
• 关键词：Mathematics Subject Classification (2000) 13D40 ; 18E30 ; 32S25
• 刊名：Mathematische Annalen
• 出版年：2010
• 出版时间：July, 2010
• 年：2010
• 卷：347
• 期：3
• 页码：689-702
• 全文大小：275.3 KB

文摘

We give a uniform and, to a large extent, geometrical proof that the Poincar¨¦ 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.