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<p>Motivated by using combinatorics to study jets of monomial ideals, we extend a definition of jets from graphs to clutters. We offer some structural results on their vertex covers and show an interesting connection between the cover ideal of the jets of a clutter and the symbolic powers of the cover ideal of the original clutter. We use this connection to prove that jets of very well-covered graphs are very well covered. Next, we turn our attention to principal jets of monomial ideals, describing their primary decomposition and minimal generating sets. Finally, we give formulas to compute various algebraic invariants of principal jets of monomial ideals, including their Hilbert series, Betti numbers, multiplicity, and regularity.</p>

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Jets and principal components of monomial ideals and very well-covered graphs

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2025年9月4日

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  • Federico Galetto,
  • Nicholas Iammarino,
  • Teresa Yu

摘要

Motivated by using combinatorics to study jets of monomial ideals, we extend a definition of jets from graphs to clutters. We offer some structural results on their vertex covers and show an interesting connection between the cover ideal of the jets of a clutter and the symbolic powers of the cover ideal of the original clutter. We use this connection to prove that jets of very well-covered graphs are very well covered. Next, we turn our attention to principal jets of monomial ideals, describing their primary decomposition and minimal generating sets. Finally, we give formulas to compute various algebraic invariants of principal jets of monomial ideals, including their Hilbert series, Betti numbers, multiplicity, and regularity.