Monomial ideals and the failure of the Strong Lefschetz property
| Autor: | Samuel Lundqvist, Nasrin Altafi |
|---|---|
| Rok vydání: | 2021 |
| Předmět: |
Monomial
Pure mathematics Hilbert series and Hilbert polynomial Property (philosophy) Forcing (recursion theory) Mathematics::Commutative Algebra Applied Mathematics General Mathematics 010102 general mathematics Monomial ideal Mathematics - Commutative Algebra Commutative Algebra (math.AC) 01 natural sciences Upper and lower bounds symbols.namesake 0103 physical sciences symbols FOS: Mathematics 13A02 13D40 13E10 010307 mathematical physics 0101 mathematics In degree Quotient Mathematics |
| DOI: | 10.48550/arxiv.2107.00497 |
| Popis: | We give a sharp lower bound for the Hilbert function in degree d of artinian quotients $$\Bbbk [x_1,\ldots ,x_n]/I$$ k [ x 1 , … , x n ] / I failing the Strong Lefschetz property, where I is a monomial ideal generated in degree $$d \ge 2$$ d ≥ 2 . We also provide sharp lower bounds for other classes of ideals, and connect our result to the classification of the Hilbert functions forcing the Strong Lefschetz property by Zanello and Zylinski. |
| Databáze: | OpenAIRE |
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