Projective Hypersurfaces of High Degree Admitting an Induced Additive Action

Bulletin of the Malaysian Mathematical Sciences Society. 2025. Vol. 48. Article 195.

Бельдиев И. С.

We study induced additive actions on projective hypersurfaces, i.e. effective regular actions of the algebraic group G_a^m with an open orbit that can be extended to a regular action on the ambient projective space. It is known that the degree of a hypersurface X in the n-dimensional projective space P^n admitting an induced additive action cannot be greater than n and there is a unique such hypersurface of degree n. We give a complete classification of hypersurfaces X ⊆ P^n admitting an induced additive action of degrees from n - 1 to n - 3.

Ключевые слова: коммутативная унипотентная группа, commutative unipotent group, local algebra, проективное пространство, локальная алгебра, projective hypersurface, проективная гиперповерхность, projective space, Gorenstein algebra, горенштейнова алгебра

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