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<p>In this paper, we provide explicit formulas for the extremal Betti numbers of <i>R</i>/<i>I</i>, where <i>I</i> is the defining ideal of certain weighted hyperplanes in <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(\mathbb {P}^{n-1}\)</EquationSource> <EquationSource Format="MATHML"><math> <msup> <mrow> <mi mathvariant="double-struck">P</mi> </mrow> <mrow> <mi>n</mi> <mo>-</mo> <mn>1</mn> </mrow> </msup> </math></EquationSource> </InlineEquation> and <i>R</i> is the polynomial ring in <i>n</i> indeterminates over a field. As a consequence, we completely classify such ideals for which the quotient ring is a pseudo-Gorenstein ring.</p>

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Extremal Betti numbers of certain two-dimensional monomial ideals

  • 期刊论文

  • 发表日期：

    2026年2月17日

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  • Nguyên Quang Lôc,
  • Nguyên Công Minh,
  • Phan Thi Thuy

摘要

In this paper, we provide explicit formulas for the extremal Betti numbers of R/I, where I is the defining ideal of certain weighted hyperplanes in \(\mathbb {P}^{n-1}\) P n - 1 and R is the polynomial ring in n indeterminates over a field. As a consequence, we completely classify such ideals for which the quotient ring is a pseudo-Gorenstein ring.