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Limits of graded Go...
Limits of graded Gorenstein algebras of Hilbert function $$(1,3^k,1)$$
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- Abdallah, Nancy (author)
- Högskolan i Borås,Akademin för textil, teknik och ekonomi
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- Emsalem, Jacques (author)
- Northeastern Univ, Dept Math, Boston
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- Iarrobino, Anthony (author)
- Northeastern Univ, Dept Math, Boston
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- Yaméogo, Joachim (author)
- Univ Cote Azur, CNRS, LJAD, Nice, France
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(creator_code:org_t)
- 2024
- 2024
- English.
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In: European Journal of Mathematics. - 2199-675X .- 2199-6768. ; 10:1
- Related links:
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https://urn.kb.se/re...
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https://doi.org/10.1...
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Abstract
Subject headings
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- Let R= k [x, y, z], the polynomial ring over a field k. Several of the authors previously classified nets of ternary conics and their specializations over an algebraically closed field, Abdallah et al. (Eur J Math 9(2), Art. No. 22, 2023). We here show that when k is algebraically closed, and considering the Hilbert function sequence T =(1,3(k),1), k >= 2 (i.e. T = (1, 3, 3, ... , 3, 1) where k is the multiplicity of 3), then the family GT parametrizing graded Artinian algebra quotients A = R/I of R having Hilbert function T is irreducible, and G(T) is the closure of the family Gor(T) of Artinian Gorenstein algebras of Hilbert function T. We then classify up to isomorphism the elements of these families Gor(T) and of G(T). Finally, we give examples of codimension 3 Gorenstein sequences, such as (1, 3, 5, 3, 1), for which G(T) has several irreducible components, one being the Zariski closure of Gor(T).
Subject headings
- NATURVETENSKAP -- Matematik -- Algebra och logik (hsv//swe)
- NATURAL SCIENCES -- Mathematics -- Algebra and Logic (hsv//eng)
Keyword
- Artinian Gorenstein algebra
- Closure
- Deformation
- Hilbert function
- Irreducible component
- Isomorphism class
- Limits
- Nets of conics
- Normal form
- Parametrization
Publication and Content Type
- ref (subject category)
- art (subject category)
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