Binomial edge ideals and rational normal scrolls

نویسندگان

  • A. Dokuyucu Faculty of Mathematics and Computer Science‎, ‎Ovidius University‎ ‎Bd‎. ‎Mamaia 124‎, ‎900527 Constanta, and Lumina-The University of South-East Europe‎ ‎Sos‎. ‎Colentina nr‎. ‎64b‎, ‎Bucharest‎, ‎Romania
  • F. Chaudhry Abdus Salam School of Mathematical Sciences‎, ‎GC University‎, ‎68-B‎, ‎New Muslim Town‎, ‎Lahore 54600‎, ‎Pakistan
  • V. Ene Faculty of Mathematics and Computer Science‎, ‎Ovidius University‎, ‎Bd.\ Mamaia 124‎, ‎900527 Constanta‎, ‎Romania‎, ‎and‎ Simion Stoilow Institute of Mathematics of the Romanian Academy‎, ‎Research group of the project ID-PCE-2011-1023‎, ‎P.O.Box 1-764‎, ‎Bucharest 014700‎, ‎Romania
چکیده مقاله:

‎Let $X=left(‎ ‎begin{array}{llll}‎ ‎ x_1 & ldots & x_{n-1}& x_n\‎ ‎ x_2& ldots & x_n & x_{n+1}‎ ‎end{array}right)$ be the Hankel matrix of size $2times n$ and let $G$ be a closed graph on the vertex set $[n].$ We study the binomial ideal $I_Gsubset K[x_1,ldots,x_{n+1}]$ which is generated by all the $2$-minors of $X$ which correspond to the edges of $G.$ We show that $I_G$ is Cohen-Macaulay‎. ‎We find the minimal primes of $I_G$ and show that $I_G$ is a set theoretical complete intersection‎. ‎Moreover‎, ‎a sharp upper bound for the regularity of $I_G$ is given‎.‎

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عنوان ژورنال

دوره 41  شماره 4

صفحات  971- 979

تاریخ انتشار 2015-08-01

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