An infinite series of Gorenstein local algebras failing the affine homogeneity property
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2026
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| _version_ | 1866911569714085888 |
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| author | Avdeev, Roman Zaitseva, Yulia |
| author_facet | Avdeev, Roman Zaitseva, Yulia |
| contents | We provide an infinite series of commutative finite-dimensional Gorenstein local algebras $A_n$ for $n \ge 2$. We give an elementary proof that the maximal ideal of every algebra $A_n$ possesses a one-dimensional subspace that is different from the socle and invariant under the automorphism group of $A_n$. The latter implies that the algebras $A_n$ fail the affine homogeneity property. We also discuss some consequences concerning additive actions on projective hypersurfaces, related to the generalized Hassett-Tschinkel correspondence for these algebras. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_04793 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | An infinite series of Gorenstein local algebras failing the affine homogeneity property Avdeev, Roman Zaitseva, Yulia Commutative Algebra Algebraic Geometry 13E10, 13H10, 14L30 We provide an infinite series of commutative finite-dimensional Gorenstein local algebras $A_n$ for $n \ge 2$. We give an elementary proof that the maximal ideal of every algebra $A_n$ possesses a one-dimensional subspace that is different from the socle and invariant under the automorphism group of $A_n$. The latter implies that the algebras $A_n$ fail the affine homogeneity property. We also discuss some consequences concerning additive actions on projective hypersurfaces, related to the generalized Hassett-Tschinkel correspondence for these algebras. |
| title | An infinite series of Gorenstein local algebras failing the affine homogeneity property |
| topic | Commutative Algebra Algebraic Geometry 13E10, 13H10, 14L30 |
| url | https://arxiv.org/abs/2604.04793 |