Almost split sequences and Zariski differentials

Abstract

ABSTRACT. Let R be a complete two-dimensional integrally closed analytic kalgebra. Associated with R is the Auslander module A from the fundamental sequence 0 -+ W R -+ A -+ R -+ k -+ 0 and the module of Zariski differentials Dk(R)** . We conjecture that these modules are isomorphic if and only if R is graded. We prove this conjecture for (a) hypersurfaces f = X; + g(X1 ' X 2 ) , (b) quotient singularities, and (c) R graded Gorenstein.