Abstract. A complete classification of all supercommutative algebras of super differential operators is established in terms of graded algebraic varieties and vector bundles on them. A geometric interpretation of all the known supersymmetric KP equations is also given in terms of vector fields on a new noncommutative Grassmannian. 0. Introduction. The purpose of this paper is to give a geometric classification of all the supercommutative algebras consisting of super differential operators. A geometric classification theorem of commutative algebras of ordinary differential operators was established in [M3]. The result is, roughly speaking, that there is
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