The geometry of representations of 3-dimensional Sklyanin algebras
Faculty of Sciences. Mathematics and Computer Science
University Hospital Antwerp
, p. 1-12
University of Antwerp
The representation scheme repnA of the 3-dimensional Sklyanin algebra A associated to a plane elliptic curve and n-torsion point contains singularities over the augmentation ideal m. We investigate the semi-stable representations of the noncommutative blow-up algebra B=A⊕mt⊕m2t2⊕... to obtain a partial resolution of the central singularity projZ(B)→specZ(A) such that the remaining singularities in the exceptional fiber determine an elliptic curve and are all of type C×C2/Zn.