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We prove a singular version of Beilinson-Bernstein localization for a complex semi-simple Lie algebra following the ideas from the positive characteristic case done in \cite{BMR2}.
On the algebraic set of singular elements in a complex simple Lie algebra
algebraic singular elements
2010/11/19
Let $G$ be a complex simple Lie group and let $\g = \hbox{\rm Lie}\,G$. Let $S(\g)$ be the $G$-module of polynomial functions on $\g$ and let $\hbox{\rm Sing}\,\g$ be the closed algebraic cone of sin...
We construct a family of measures on $\bbR$ that are purely singular with respect to Lebesgue measure, and yet exhibit universal sine-kernel asymptotics in the bulk. The measures are best described v...
On representation of the P-Q pair solution at the singular point neighborhood
the P-Q pair solution singular point
2010/11/1
The compatible expansion in series of solutions of both the equations of P-Q pair at neighborhood of the singular point is obtained in closed form for regular and irregular singularities. The conserva...
A formula for Euler characteristic of line singularities on singular spaces
Euler characteristic line singularities singular spaces
2010/10/29
We prove an algebraic formula for the Euler characteristic of the Milnor fibres of functions with critical locus a smooth curve on a space which is a weighted homogeneous complete intersection with is...