On the Relation Type of Fiber Cone

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• 作者：A. V. Jayanthan ; Ramakrishna Nanduri
• 关键词：Relation type ; Fiber cone ; Rees algebra ; Associated graded ring ; Lexsegment ideal ; Equimultiple ideal ; Deviation ; Primary 13A30 ; Secondary 13A02
• 刊名：Acta Mathematica Vietnamica
• 出版年：2015
• 出版时间：September 2015
• 年：2015
• 卷：40
• 期：3
• 页码：535-544
• 全文大小：246 KB
• 参考文献：1.Conca, A., De Negri, E., Jayanthan, A.V., Rossi, M.E.: Graded rings associated with contracted ideals. J. Algebra 284, 593鈥?26 (2005)MATH MathSciNet CrossRef
  2.Conca, A., De Negri, E., Rossi, M.E.: Contracted ideals and the Gr枚bner fan of the rational normal curve. Algebra Number Theory 1(3), 239鈥?68 (2007)MATH MathSciNet CrossRef
  3.Cortadellas, T.: Depth formulas for the Rees algebras of filtrations. Commun. Algebra 24(2), 705鈥?15 (1996)MATH MathSciNet CrossRef
  4.Cortadellas, T.: Fiber cones with almost maximal depth. Commun. Algebra 33 (3), 953鈥?63 (2005)MATH MathSciNet CrossRef
  5.Cortadellas, T., Zarzuela, Z.: Depth formulas for certain graded modules associated to a filtration: a survey. Geometric and combinatorial aspects of commutative algebra (Messina, 1999), 145鈥?57, Lecture Notes in Pure and Appl. Math., 217, Dekker, New York (2001)
  6.Cortadellas, T., Zarzuela, S.: On the depth of the fiber cone of filtrations. J. Algebra 198(2), 428鈥?45 (1997)MATH MathSciNet CrossRef
  7.Heinzer, W.J., Kim, M.-K.: Properties of the fiber cone of ideals in local rings. Comm. Algebra 31(7), 3529鈥?546 (2003)MATH MathSciNet CrossRef
  8.Heinzer, W., Kim, M.-K., Ulrich, B.: The Gorenstein and complete intersection properties of associated graded rings. J. Pure Appl. Algebra 201, 264鈥?83 (2005)MATH MathSciNet CrossRef
  9.Hong, J., Simis, A., Vasconcelos, W.V.: The equations of almost complete intersections. Bull. Braz. Math. Soc. (N.S.) 43(2), 171鈥?99 (2012)MATH MathSciNet CrossRef
  10.Huckaba, S.: Reduction numbers for ideals of higher analytic spread. Math. Proc. Camb. Philos. Soc. 102(1), 49鈥?7 (1987)MATH MathSciNet CrossRef
  11.Huckaba, S.: On complete d-sequences and the defining ideals of Rees algebras. Math. Proc. Camb. Philos. Soc. 106, 445鈥?58 (1989)MATH MathSciNet CrossRef
  12.Mui帽os, F., Planas-Vilanova, F.: The equations of Rees algebras of equimultiple ideals of deviation one. Proc. Am. Math. Soc. 141(4), 1241鈥?254 (2013)MATH CrossRef
  13.Planas-Vilanova, F.: On the module of effective relations of a standard algebra. Math. Proc. Camb. Philos. Soc. 124, 215鈥?29 (1998)MATH MathSciNet CrossRef
  14.Rossi, M.E., Valla, G.: Hilbert functions of filtered modules, lecture notes of the Unione Matematica Italiana, 9. Springer, Berlin. UMI, Bologna (2010) xviii+100pp
  15.Schenzel, P.: Castelnuovo鈥檚 index of regularity and reduction numbers. In: Topics in algebra, Part II, pp 201鈥?08. Banach center Publication 26, Warsaw (1990)
  16.Trung, N.V.: Reduction exponent and degree bound for the defining equations of graded rings. Proc. Am. Math. Soc. 101(2), 229鈥?36 (1987)MATH MathSciNet CrossRef
  17.Trung, N.V.: The Castelnuovo regularity of the Rees algebra and the associated graded ring. Trans. Am. Math. Soc. 350(7), 2813鈥?832 (1998)MATH CrossRef
  18.Valla, G.: On the symmetric and Rees algebras of an ideal. Manuscr. Math. 30 (3), 239鈥?55 (1980)MATH MathSciNet CrossRef
  19.Vasconcelos, W.V.: On the equations of Rees algebras. J. Reine Angew. Math. 418, 189鈥?18 (1991)MATH MathSciNet
  
• 作者单位：A. V. Jayanthan (1)
  Ramakrishna Nanduri (2)
  
  1. Department of Mathematics, Indian Institute of Technology Madras, Chennai, 600036, India
  2. Department of Mathematics, Indian Institute of Technology Kharagpur, Kharagpur, West Bengal, 721302, India
  
• 刊物主题：Mathematics, general;
• 出版者：Springer Singapore
• ISSN：2315-4144

文摘

In this article, we study the relation type of the fiber cone of certain special classes of ideals in Noetherian local rings. We show that in any Noetherian local ring, if deviation of I is 1, and depth\((G(\mathcal F_{L})) \geq \ell -1\), then the relation types of \(\mathcal {R}(I)\) and F _L (I) are equal. We also prove that for lexsegment ideals in K[x,y], where K is a field, the relation types of the fiber cone and the Rees algebra are equal. Keywords Relation type Fiber cone Rees algebra Associated graded ring Lexsegment ideal Equimultiple ideal Deviation