대한수학회지 (Journal of the Korean Mathematical Society)

  • 제54권5호
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  • Pages.1379-1410
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  • 2017
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  • 0304-9914(pISSN)
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  • 2234-3008(eISSN)
대한수학회 (Korean Mathematical Society)
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HILBERT FUNCTIONS OF STANDARD k-ALGEBRAS DEFINED BY SKEW-SYMMETRIZABLE MATRICES

  • Kang, Oh-Jin (Department of General Studies School of Liberal Arts and Sciences Korea Aerospace University)
  • 투고 : 2015.07.06
  • 심사 : 2016.12.26
  • 발행 : 2017.09.01
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초록

Kang and Ko introduced a skew-symmetrizable matrix to describe a structure theorem for complete intersections of grade 4. Let $R=k[w_0,\;w_1,\;w_2,\;{\ldots},\;w_m]$ be the polynomial ring over an algebraically closed field k with indetermiantes $w_l$ and deg $w_l=1$, and $I_i$ a homogeneous perfect ideal of grade 3 with type $t_i$ defined by a skew-symmetrizable matrix $G_i(1{\leq}t_i{\leq}4)$. We show that for m = 2 the Hilbert function of the zero dimensional standard k-algebra $R/I_i$ is determined by CI-sequences and a Gorenstein sequence. As an application of this result we show that for i = 1, 2, 3 and for m = 3 a Gorenstein sequence $h(R/H_i)=(1,\;4,\;h_2,\;{\ldots},\;h_s)$ is unimodal, where $H_i$ is the sum of homogeneous perfect ideals $I_i$ and $J_i$ which are geometrically linked by a homogeneous regular sequence z in $I_i{\cap}J_i$.

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참고문헌

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