Waldschmidt constant of monomial ideals and Simis ideals
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arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866918265083658240 |
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| author | Bijender Kumar, Ajay |
| author_facet | Bijender Kumar, Ajay |
| contents | In 2017, Cooper et al. proposed a conjecture providing a lower bound for the Waldschmidt constant of monomial ideals. We confirm this conjecture for some classes of monomial ideals. Recently, Méndez, Pinto, and Villarreal formulated a conjecture stating that if $I$ is a monomial ideal without embedded associated primes, whose irreducible decomposition is minimal and which is a Simis ideal, then there exist a Simis squarefree monomial ideal $J$ and a standard linear weighting $w$ such that $I = J_{w}.$ In this work, we verify this conjecture for some classes of monomial ideals. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_22940 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Waldschmidt constant of monomial ideals and Simis ideals Bijender Kumar, Ajay Commutative Algebra Combinatorics 13C70, 05E40, 13A70, 13F20 In 2017, Cooper et al. proposed a conjecture providing a lower bound for the Waldschmidt constant of monomial ideals. We confirm this conjecture for some classes of monomial ideals. Recently, Méndez, Pinto, and Villarreal formulated a conjecture stating that if $I$ is a monomial ideal without embedded associated primes, whose irreducible decomposition is minimal and which is a Simis ideal, then there exist a Simis squarefree monomial ideal $J$ and a standard linear weighting $w$ such that $I = J_{w}.$ In this work, we verify this conjecture for some classes of monomial ideals. |
| title | Waldschmidt constant of monomial ideals and Simis ideals |
| topic | Commutative Algebra Combinatorics 13C70, 05E40, 13A70, 13F20 |
| url | https://arxiv.org/abs/2512.22940 |