On the Hilbert function of Gorenstein algebras of socle degree four
| Autor: | Armando Cerminara, Rodrigo Gondim, Giuseppe Zappalà, Giovanna Ilardi |
|---|---|
| Přispěvatelé: | Cerminara, Armando, Gondim, Rodrigo, Ilardi, Giovanna, Zappalà, Giuseppe |
| Jazyk: | angličtina |
| Rok vydání: | 2020 |
| Předmět: |
Hilbert series and Hilbert polynomial
Pure mathematics Mathematics::Combinatorics Algebra and Number Theory Conjecture Mathematics::Commutative Algebra Degree (graph theory) Generalization 010102 general mathematics 01 natural sciences {Hilbert Function no unimodal $h$-vector Full Perazzo Algebra Turan Algebra Socle symbols.namesake Simple (abstract algebra) 0103 physical sciences symbols 010307 mathematical physics 0101 mathematics Mathematics |
| Popis: | The first example of a non unimodal Gorenstein h-vector was given by Stanley, it is ( 1 , 13 , 12 , 13 , 1 ) . In [14] the authors showed that Stanley's example is optimal, i.e., the vector ( 1 , 12 , 11 , 12 , 1 ) is not a Gorenstein h-vector. Our main result is a generalization of this result. We also give a simple proof of Stanley's conjecture on the asymptotic behavior of the Hilbert function in socle degree four. We present a conjecture about the asymptotic behavior of the Hilbert function for those algebras that are presented by quadrics. |
| Databáze: | OpenAIRE |
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