McKay correspondence for Kleinian and Fuchsian singularities via spherical twists

From CRCG-Wiki

David Ploog (joint with Wolfgang Ebeling)

To Kleinian and (certain) Fuchsian singularities, one can associate Poincare series. We give a conceptual proof of the fact that these series are quotients of the characteristic polynomials of appropriately chosen Coxeter elements. The main idea is to lift all data from the K-theoretic level to sheaves and derived categories.