CW-complexes and minimal Hilbert vector of graded Artinian Gorenstein algebras
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866912916665532416 |
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| author | Capasso, Armando |
| author_facet | Capasso, Armando |
| contents | I introduce a geometric interpretation of the set of standard graded Artinian Gorenstein algebras of codimension n and degree d: the standard locus, which is a subset of the projective space of degree d polynomials in n variables, and I characterize it. Under opportune hypothesis, I prove that the locus of full Perazzo polynomials is the union of the minimal dimensional irreducible components of the standard locus and it is a pure dimensional subset. On the other hand, I associate to any homogeneous polynomial a topological space, which is a CW-complex. Using all these sets, I prove that the Hilbert function restricted to the standard locus has minimal values on any irreducible component of the domain. I apply all this to the Full Perazzo Conjecture and I prove it. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_13276 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | CW-complexes and minimal Hilbert vector of graded Artinian Gorenstein algebras Capasso, Armando Commutative Algebra Combinatorics Rings and Algebras I introduce a geometric interpretation of the set of standard graded Artinian Gorenstein algebras of codimension n and degree d: the standard locus, which is a subset of the projective space of degree d polynomials in n variables, and I characterize it. Under opportune hypothesis, I prove that the locus of full Perazzo polynomials is the union of the minimal dimensional irreducible components of the standard locus and it is a pure dimensional subset. On the other hand, I associate to any homogeneous polynomial a topological space, which is a CW-complex. Using all these sets, I prove that the Hilbert function restricted to the standard locus has minimal values on any irreducible component of the domain. I apply all this to the Full Perazzo Conjecture and I prove it. |
| title | CW-complexes and minimal Hilbert vector of graded Artinian Gorenstein algebras |
| topic | Commutative Algebra Combinatorics Rings and Algebras |
| url | https://arxiv.org/abs/2502.13276 |