Saved in:
| Main Author: | |
|---|---|
| Format: | Preprint |
| Published: |
2025
|
| Subjects: | |
| Online Access: | https://arxiv.org/abs/2511.17169 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866912723072188416 |
|---|---|
| author | Kaygun, Atabey |
| author_facet | Kaygun, Atabey |
| contents | We provide a unified geometric realization of the classical deformation complexes. We construct GL-equivariant bilinear incidence varieties whose diagonal slices recover the varieties of associative, commutative, Leibniz, and Lie algebra structures on a finite-dimensional vector space. We prove that the fiber of the incidence map at a given algebra law is canonically isomorphic to the space of 2-cocycles in the corresponding cohomology theory (Hochschild, Harrison, Leibniz, or Chevalley--Eilenberg). Furthermore, we introduce invariant bilinear forms to define open strata of separable and semisimple algebras, and demonstrate that these strata consist of open GL-orbits, establishing the rigidity of generic points in the coarse moduli spaces for all four geometries. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_17169 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Geometry of Deformations via Incidence Varieties Kaygun, Atabey Rings and Algebras Algebraic Geometry K-Theory and Homology 16S80, 16E40, 17A32, 17B56, 17B20 We provide a unified geometric realization of the classical deformation complexes. We construct GL-equivariant bilinear incidence varieties whose diagonal slices recover the varieties of associative, commutative, Leibniz, and Lie algebra structures on a finite-dimensional vector space. We prove that the fiber of the incidence map at a given algebra law is canonically isomorphic to the space of 2-cocycles in the corresponding cohomology theory (Hochschild, Harrison, Leibniz, or Chevalley--Eilenberg). Furthermore, we introduce invariant bilinear forms to define open strata of separable and semisimple algebras, and demonstrate that these strata consist of open GL-orbits, establishing the rigidity of generic points in the coarse moduli spaces for all four geometries. |
| title | Geometry of Deformations via Incidence Varieties |
| topic | Rings and Algebras Algebraic Geometry K-Theory and Homology 16S80, 16E40, 17A32, 17B56, 17B20 |
| url | https://arxiv.org/abs/2511.17169 |