Weak Lefschetz property of equigenerated complete intersections. Applications
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866908280036524032 |
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| author | Beorchia, Valentina Miró-Roig, Rosa Maria |
| author_facet | Beorchia, Valentina Miró-Roig, Rosa Maria |
| contents | In this paper, we prove that any Artinian complete intersection homogeneous ideal $I$ in $K[x_0,\cdots,x_n]$ generated by $n+1$ forms of degree $d\ge 2$ satisfies the weak Lefschetz property (WLP) in degree $t< d+\lceil \frac{d}{n} \rceil$. As a consequence, we get that the Jacobian ideal of a smooth 3-fold of degree $d\ge 7$ in ${\mathbb P}^4$ satisfies the weak Lefschetz property in degree $d$, answering a recent question of Beauville. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_17991 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Weak Lefschetz property of equigenerated complete intersections. Applications Beorchia, Valentina Miró-Roig, Rosa Maria Algebraic Geometry 13E10, 14M10, 14F06 In this paper, we prove that any Artinian complete intersection homogeneous ideal $I$ in $K[x_0,\cdots,x_n]$ generated by $n+1$ forms of degree $d\ge 2$ satisfies the weak Lefschetz property (WLP) in degree $t< d+\lceil \frac{d}{n} \rceil$. As a consequence, we get that the Jacobian ideal of a smooth 3-fold of degree $d\ge 7$ in ${\mathbb P}^4$ satisfies the weak Lefschetz property in degree $d$, answering a recent question of Beauville. |
| title | Weak Lefschetz property of equigenerated complete intersections. Applications |
| topic | Algebraic Geometry 13E10, 14M10, 14F06 |
| url | https://arxiv.org/abs/2503.17991 |