Segre Product, H-Polynomials, and Castelnuovo-Mumford Regularity

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• 作者：Marcel Morales (1)
  Nguyen Thi Dung (2)
  
  1. Institut Fourier ; UMR 5582 ; B.P.74 ; 38402 Saint-Martin D鈥橦猫res Cedex ; and IUFM de Lyon ; Universit茅 de Grenoble I ; 5 rue Anselme ; 69317 ; Lyon Cedex ; France
  2. Thai Nguyen University of Agriculture and Forestry ; Thai Nguyen ; Vietnam
  
• 关键词：Segre ; Veronese ; Castelnuovo ; Mumford regularity ; Cohen ; Macaulay modules ; Postulation number ; Eulerian polynomial ; Simon Newcomb problem ; Primary ; 13D40 ; Secondary 14M25 ; 13C14 ; 14M05
• 刊名：Acta Mathematica Vietnamica
• 出版年：2015
• 出版时间：March 2015
• 年：2015
• 卷：40
• 期：1
• 页码：111-124
• 全文大小：408 KB
• 参考文献：1. Barcanescu, S, Manolache, N (1979) Nombres de Betti d鈥檜ne singularite de Segre-Verones茅. C. R. Acad. Sci. Paris, S茅r. A 288: pp. 237-239
  2. Bacanescu, S, Manolache, N (1981) Betti numbers of Segre-Veronese singularities. Rev. Roum. Math. Pures Appl. 26: pp. 549-565
  3. Brenti, F (2009) The Veronese construction for formal power series and graded algebras. Adv. in Appl. Math. 42: pp. 545-556 CrossRef
  4. Cox, David A., Materov, E.: Regularity and Segre-Veronese embeddings. Proc. Am. Math. Soc. 137(6), 1883鈥?890 (2009)
  5. Diaconis, P, Fulman, J (2009) Carries, shuffling, and symmetric functions. Adv. in Appl. Math. 43: pp. 176-196 CrossRef
  6. Fischer, I., Kubitzke, M.: Spectra and eigenvectors of the Segre transformation. arXiv:1303.5358 (2013)
  7. Goto, S, Watanabe, K (1978) On graded rings. I. J. Math. Soc. Japan 30: pp. 179-213 CrossRef
  8. MacMahon, PA (1960) Combinatorial Analysis. Vol. I, II bound in one volume. Chelsea Publishing Company, New York
  9. Marcel, M.: Fonctions de Hilbert, genre g茅om茅trique d鈥檜ne singularit茅 quasi-homog猫ne Cohen-Macaulay. CRAS Paris, t.301, s茅rie A / n ^{/ o} 14 (1985)
  10. Marcel, M.: Segre embeddings, Hilbert series and Newcomb鈥檚 problem. arXiv:1306.6910 (2013)
  11. Marcel, M., Dung, N.T.: Castelnuovo-Mumford regularity of classical rings and Veronese transform. Preprint (2013)
  12. St眉ckrad, J., Vogel, W.: Buchsbaum rings and applications. An interaction between algebra, geometry, and topology. Monographien, Mathematische, Bd. 21. Berlin: VEB Deutscher Verlag der Wissenschaften. 286 (1986)
  13. Sturmfels, B.: Grobner bases and convex polytopes. University Lecture Series. 8. Providence, RI: American Mathematical Society (AMS). xi, p 162 (1996)
  
• 刊物主题：Mathematics, general;
• 出版者：Springer Singapore
• ISSN：2315-4144

文摘

The purpose of this paper is to extend the bilinearity of the Segre product that has been proved recently by Ilse Fischer and Martina Kubitzke under some restricted hypotheses. As a consequence, we get some formulas involving Eulerian polynomials and a nice formula that will be used by the first author to solve the Simon Newcomb problem. We apply these results to compute the postulation number of a series and extend partially the results about Castelnuovo-Mumford regularity of the Segre product of polynomial rings of David A. Cox and Evgeny Materov.