Igor Dolgachev studies algebraic geometry, including the classical geometry of plane curves and their symmetries. With Michela Artebani, he wrote a study of the Hesse pencil and its associated configurations.[ref]
The Hesse pencil of plane cubic curves by Michela Artebani and Igor Dolgachev. Original author byline, abstract and section 2
The pencil combines plane cubic algebraic curves sharing nine base points. Those points encode the flex geometry of a smooth cubic, while special members split into lines. The paper connects this classical configuration with elliptic surfaces and K3 surfaces, illustrating how a one-parameter family of equations organizes several geometric objects at once.[ref]
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Igor Dolgachev is a mathematician known for his contributions to various fields, including algebraic geometry and algebra. He is recognized for his work on algebraic groups, automorphic forms, and related areas. Dolgachev has published numerous papers and is often cited in mathematical literature.