The Geometry of Representations of 3-Dimensional Sklyanin Algebras

Abstract

The representation scheme rep (n) A of the 3-dimensional Sklyanin algebra A associated to a plane elliptic curve and n-torsion point contains singularities over the augmentation ideal oe"(a). We investigate the semi-stable representations of the noncommutative blow-up algebra B = A aS center dot oe"(a)t aS center dot oe"(a2) t (2) aS center dot aEuro broken vertical bar to obtain a partial resolution of the central singularity such that the remaining singularities in the exceptional fiber determine an elliptic curve and are all of type a", x a",(2)/a"currency sign (n) .