Singular Poisson–Kähler geometry of certain adjoint quotients
Volume 76 / 2007
Banach Center Publications 76 (2007), 325-347
MSC: Primary 17B63, 17B65, 17B66, 17B81, 53D17, 53D20,
55R80; Secondary 14L24, 16W22, 32S60,
70H45.
DOI: 10.4064/bc76-0-16
Abstract
The Kähler quotient of a complex reductive Lie group relative to the conjugation action carries a complex algebraic stratified Kähler structure which reflects the geometry of the group. For the group ${\rm SL}(n,\mathbb C)$, we interpret the resulting singular Poisson-Kähler geometry of the quotient in terms of complex discriminant varieties and variants thereof.
