Arithmetical rank of lexsegment edge ideals

作者: Viviana Ene , Naoki Terai , Oana Olteanu

DOI:

关键词:

摘要: Let $I\subset S=K[x_1,...,x_n]$ be a lexsegment edge ideal or the Alexander dual of such an ideal. In both cases it turns out that arithmetical rank $I$ is equal to projective dimension $S/I.$

参考文章(14)
Giuseppe Valla, On set-theoretic complete intersections Springer Berlin Heidelberg. pp. 85- 101 ,(1984) , 10.1007/BFB0099358
L. Sorrenti, M. Bonanzinga, L. Sorrentino, Squarefree lexsegment ideals with linear resolution Bollettino Della Unione Matematica Italiana. ,vol. 1, pp. 275- 292 ,(2008)
Gennady Lyubeznik, On the local cohomology modules for ideals generated by monomials in an R-sequence Springer, Berlin, Heidelberg. pp. 214- 220 ,(1984) , 10.1007/BFB0099364
Kyouko Kimura, Naoki Terai, Ken-ichi Yoshida, Arithmetical rank of squarefree monomial ideals of small arithmetic degree Journal of Algebraic Combinatorics. ,vol. 29, pp. 389- 404 ,(2009) , 10.1007/S10801-008-0142-3
Thomas Schmitt, Wolfgang Vogel, Note on set-theoretic intersections of subvarieties of projective space Mathematische Annalen. ,vol. 245, pp. 247- 253 ,(1979) , 10.1007/BF01673509
Hans-Gert Gräbe, Über den arithmetischen Rang quadratfreier Potenzproduktideale Mathematische Nachrichten. ,vol. 120, pp. 217- 227 ,(1985) , 10.1002/MANA.19851200118
Gil Kalai, Roy Meshulam, Intersections of Leray complexes and regularity of monomial ideals Journal of Combinatorial Theory, Series A. ,vol. 113, pp. 1586- 1592 ,(2006) , 10.1016/J.JCTA.2006.01.005
Annetta Aramova, Jürgen Herzog, Takayuki Hibi, Squarefree lexsegment ideals Mathematische Zeitschrift. ,vol. 228, pp. 353- 378 ,(1998) , 10.1007/PL00004621
Jürgen Herzog, A Generalization of the Taylor Complex Construction Communications in Algebra. ,vol. 35, pp. 1747- 1756 ,(2007) , 10.1080/00927870601139500
Margherita Barile, Naoki Terai, The Stanley-Reisner ideals of polygons as set-theoretic complete intersections arXiv: Commutative Algebra. ,(2009)