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Journal of the London Mathematical Society 1996 53(3):464-478; doi:10.1112/jlms/53.3.464
© 1996 by London Mathematical Society
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© The London Mathematical Society

Linear Modules over Sklyanin Algebras

Joanna M. Staniszkis

Department of Mathematics, Texas A&M University College Station, Texas 77843, USA

Received 13 December 1993. Revision received 3 June 1994.

Let A = An(E, {tau}) be the n-dimensional Sklyanin algebra associated with a smooth elliptic curve E and point {tau} isin E. This paper classifies linear modules over A. We show that d-linear modules are in bijection with those d-planes in P(Formula) which are either secant to E or are singular loci of certain rank (n — d — 1)-quadrics containing E. Moreover, linear modules are Cohen-Macaulay and critical, and non-isomorphic linear modules give non-isomorphic linear spaces in Proj A. We also construct all short exact sequences of linear modules.

Current address: Department of Mathematics, University of Michigan, Ann Arbor, Michigan 48109, USA E-mail: staniszk{at}math.lsa.umich.edu


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