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Yury Volkov (wolf86 666@list.ru).Abstract. The work is devoted to the variety of 2-dimensional algebras over an algebraically closed field. Firstly, we classify such algebras modulo isomorphism. Then we describe the degenerations and the closures of certain algebra series in the variety of 2-dimensional algebras. Finally, we apply our results to obtain analogous descriptions for the subvarieties of flexible, and bicommutative algebras. In particular, we describe rigid algebras and irreducible components for these subvarieties.

), Alexandre Pozhidaev (app@math.nsc.ru), Yury Volkov (wolf86 666@list.ru).Abstract. We describe degenerations of four-dimensional Zinbiel and four-dimensional nilpotent Leibniz algebras over C. In particular, we describe all irreducible components in the corresponding varieties.

Yury Volkov (wolf86 666@list.ru).Abstract. We describe degenerations of four-dimensional binary Lie algebras, and five-and six-dimensional nilpotent Malcev algebras over C. In particular, we describe all irreducible components of these varieties.

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