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arXiv · 2512.22940

Waldschmidt constant of monomial ideals and Simis ideals

Bijender·Ajay Kumar
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Abstract

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, M\'endez, 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.

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Bijender, Ajay Kumar. 2025-12-28. Waldschmidt constant of monomial ideals and Simis ideals. https://arxiv.org/abs/2512.22940

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