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Volumn 359, Issue 10, 2007, Pages 4711-4727

Mixed multiplicities of ideals versus mixed volumes of polytopes

Author keywords

Diagonal algebra; Hilbert functions of multigraded algebras; Mixed multiplicities; Mixed volume; Multigraded Rees algebra; Toric rings

Indexed keywords


EID: 48849099544     PISSN: 00029947     EISSN: None     Source Type: Journal    
DOI: 10.1090/S0002-9947-07-04054-8     Document Type: Article
Times cited : (49)

References (36)
  • 1
    • 0001669520 scopus 로고
    • The Hilbert function of two ideals
    • MR0089835 (19:727b)
    • P.B. Bhattacharya, The Hilbert function of two ideals, Proc. Cambridge Phil. Soc. 53 (1957), 568-575. MR0089835 (19:727b)
    • (1957) Proc. Cambridge Phil. Soc. , vol.53 , pp. 568-575
    • Bhattacharya, P.B.1
  • 2
    • 0000503187 scopus 로고
    • The number of roots of a system of equations (Russian)
    • MR0435072 (55:8034)
    • D.N. Bernstein, The number of roots of a system of equations (Russian), Funkcional. Anal. i PriloZen. 9 (1975), no. 3, 1-4. MR0435072 (55:8034)
    • (1975) Funkcional. Anal. i PriloZen. , vol.9 , Issue.3 , pp. 1-4
    • Bernstein, D.N.1
  • 4
    • 0003363898 scopus 로고    scopus 로고
    • Cohen-macaulay rings
    • Revised Edition Cambridge University Press, Cambridge MR1251956 (95h:13020)
    • W. Bruns and J. Herzog, Cohen-Macaulay Rings, Revised Edition, Cambridge Studies in Advanced Mathematics, 39. Cambridge University Press, Cambridge, 1998. MR1251956 (95h:13020)
    • (1998) Cambridge Studies in Advanced Mathematics , vol.39
    • Bruns, W.1    Herzog, J.2
  • 5
    • 0001520688 scopus 로고    scopus 로고
    • Diagonal subalgebras of bigraded algebras and embeddings of blow-ups of projective spaces
    • A. Conca, J. Herzog, N.V. Trung and G. Valla, Diagonal subalgebras of bigraded algebras and embeddings of blow-ups of projective spaces, American Journal of Math. 119 (1997), 859-901. MR1465072 (99d:13001) (Pubitemid 127370272)
    • (1997) American Journal of Mathematics , vol.119 , Issue.4 , pp. 859-901
    • Conca, A.1    Herzog, J.2    Trung, N.V.3    Valla, G.4
  • 7
    • 0000348667 scopus 로고
    • Efficient incremental algorithms for the sparse resultant and the mixed volume
    • MR1374227 (96j:68098)
    • I. Emiris and J. Canny, Efficient incremental algorithms for the sparse resultant and the mixed volume, J. Symbolic Comput. 20 (1995), 117-149. MR1374227 (96j:68098)
    • (1995) J. Symbolic Comput. , vol.20 , pp. 117-149
    • Emiris, I.1    Canny, J.2
  • 9
    • 0041046181 scopus 로고
    • Die Satze von Bertini fur lokale Ringe
    • MR0460317 (57:311)
    • H. Flenner, Die Satze von Bertini fur lokale Ringe, Math. Ann. 229 (1977), 97-111. MR0460317 (57:311)
    • (1977) Math. Ann. , vol.229 , pp. 97-111
    • Flenner, H.1
  • 10
    • 0004233493 scopus 로고
    • Springer-Verlag, Berlin-Heidelberg MR0732620 (85k:14004)
    • W. Fulton, Intersection theory, Springer-Verlag, Berlin-Heidelberg, 1984. MR0732620 (85k:14004)
    • (1984) Intersection Theory
    • Fulton, W.1
  • 11
    • 0002893741 scopus 로고
    • Introduction to toric varieties
    • Princeton University Press MR1234037 (94g:14028)
    • W. Fulton, Introduction to toric varieties, Annals ofMathematics Studies, 131, Princeton University Press, 1993. MR1234037 (94g:14028)
    • (1993) Annals of Mathematics Studies , vol.131
    • Fulton, W.1
  • 13
    • 84968520678 scopus 로고
    • A polyhedral method for solving sparse polynomial equations
    • MR1297471 (95m:65100)
    • B. Huber and B. Sturmfels, A polyhedral method for solving sparse polynomial equations, Math. of Computation 64 (1995), 1541-1555. MR1297471 (95m:65100)
    • (1995) Math. of Computation , vol.64 , pp. 1541-1555
    • Huber, B.1    Sturmfels, B.2
  • 14
    • 0031543232 scopus 로고    scopus 로고
    • Bernstein's theorem in affine spaces
    • MR1424821 (98b:52014)
    • B. Huber and B. Sturmfels, Bernstein's theorem in affine spaces, Discrete. Comput. Geom. 19 (1997), 137-141. MR1424821 (98b:52014)
    • (1997) Discrete. Comput. Geom. , vol.19 , pp. 137-141
    • Huber, B.1    Sturmfels, B.2
  • 15
    • 0011055659 scopus 로고
    • Hilbert function of bigraded algebras
    • A. Simis, N.V. Trung and G. Valla (eds.) World Scientific MR1421092 (97h:13013)
    • D. Katz, S. Mandal and J. Verma, Hilbert function of bigraded algebras, in: A. Simis, N.V. Trung and G. Valla (eds.), Commutative Algebra (ICTP, Trieste, 1992), 291-302, World Scientific, 1994. MR1421092 (97h:13013)
    • (1994) Commutative Algebra (ICTP, Trieste, 1992) , pp. 291-302
    • Katz, D.1    Mandal, S.2    Verma, J.3
  • 16
    • 0001194450 scopus 로고
    • Extended Rees algebras and mixed multiplicities
    • MR1007742 (90i:13024)
    • D. Katz and J. Verma, Extended Rees algebras and mixed multiplicities, Math. Z. 202 (1989), 111-128. MR1007742 (90i:13024)
    • (1989) Math. Z. , vol.202 , pp. 111-128
    • Katz, D.1    Verma, J.2
  • 17
    • 0000738611 scopus 로고
    • Newton polytopes and toric varieties
    • MR0476733 (57:16291)
    • A.G. Khovanski, Newton polytopes and toric varieties, Functional Anal. Appl. 11 (1977), 289-298. MR0476733 (57:16291)
    • (1977) Functional Anal. Appl. , vol.11 , pp. 289-298
    • Khovanski, A.G.1
  • 18
    • 0039930339 scopus 로고
    • Newton polytopes and Bezout theorem
    • MR0422272 (54:10263)
    • A.G. Kuschnirenko, Newton polytopes and Bezout theorem, Functional Anal. Appl. 10 (1976), 233-235. MR0422272 (54:10263)
    • (1976) Functional Anal. Appl. , vol.10 , pp. 233-235
    • Kuschnirenko, A.G.1
  • 19
    • 0001815166 scopus 로고
    • A-transforms of local rings and a theorem on multiplicities of ideals
    • MR0118750 (22:9521)
    • D. Rees, a-transforms of local rings and a theorem on multiplicities of ideals, Proc. Cambridge Philos. Soc. 57 (1961), 8-17. MR0118750 (22:9521)
    • (1961) Proc. Cambridge Philos. Soc. , vol.57 , pp. 8-17
    • Rees, D.1
  • 20
    • 0242341986 scopus 로고
    • Generalizations of reductions and mixed multiplicities
    • MR0754926 (86e:13023)
    • D. Rees, Generalizations of reductions and mixed multiplicities, J. London Math. Soc. 29 (1984), 423-432. MR0754926 (86e:13023)
    • (1984) J. London Math. Soc. , vol.29 , pp. 423-432
    • Rees, D.1
  • 21
    • 0011354399 scopus 로고
    • Local Chern classes, multiplicities and perfect complexes
    • MR1044350 (91d:13025)
    • P. Roberts, Local Chern classes, multiplicities and perfect complexes, Memoire Soc. Math. France 38 (1989), 145-161. MR1044350 (91d:13025)
    • (1989) Memoire Soc. Math. France , vol.38 , pp. 145-161
    • Roberts, P.1
  • 22
    • 0039510572 scopus 로고
    • On a theorem of B. Teissier on mixed multiplicities of ideals in local rings
    • MR0518229 (80e:13009)
    • D. Rees and R.Y. Sharp, On a theorem of B. Teissier on mixed multiplicities of ideals in local rings, J. London Math. Soc. 18 (1978), 449-463. MR0518229 (80e:13009)
    • (1978) J. London Math. Soc. , vol.18 , pp. 449-463
    • Rees, D.1    Sharp, R.Y.2
  • 24
    • 0242632579 scopus 로고    scopus 로고
    • Solving systems of polynomial equations
    • American Mathematical Society MR1925796 (2003i:13037)
    • B. Sturmfels, Solving systems of polynomial equations, CBMS Regional Conference Series in Mathematics, No. 97, American Mathematical Society, 2002. MR1925796 (2003i:13037)
    • (2002) CBMS Regional Conference Series in Mathematics , Issue.97
    • Sturmfels, B.1
  • 25
    • 0004079059 scopus 로고
    • VEB Deutscher Verlag der Wisssenschaften, Berlin MR0881220 (88h:13011b)
    • J. Stuckrad and W. Vogel, Buchsbaum rings and applications, VEB Deutscher Verlag der Wisssenschaften, Berlin, 1986. MR0881220 (88h:13011b)
    • (1986) Buchsbaum Rings and Applications
    • Stuckrad, J.1    Vogel, W.2
  • 26
    • 84963011709 scopus 로고
    • Mixed multiplicities, joint reductions and quasi-unmixed local rings
    • MR1223888 (94d:13027)
    • I. Swanson, Mixed multiplicities, joint reductions and quasi-unmixed local rings, J. London Math. Soc. 48 (1993), 1-14. MR1223888 (94d:13027)
    • (1993) J. London Math. Soc. , vol.48 , pp. 1-14
    • Swanson, I.1
  • 27
    • 0001092305 scopus 로고
    • Cycles evanescents, sections planes, et conditions de Whitney
    • Asterisque MR0374482 (51:10682)
    • B. Teissier, Cycles evanescents, sections planes, et conditions de Whitney, Singularites aCargese 1972, Asterisque 7-8 (1973), 285-362. MR0374482 (51:10682)
    • (1973) Singularites A Cargese 1972 , vol.7-8 , pp. 285-362
    • Teissier, B.1
  • 28
    • 0013092272 scopus 로고
    • Sur un inegalite a la Minkowski pour les multiplicites (Appendix to a paper by D. Eisenbud and H.I. Levine)
    • MR0467800 (57:7651)
    • B. Teissier, Sur un inegalite a la Minkowski pour les multiplicites (Appendix to a paper by D. Eisenbud and H.I. Levine), Ann. of Math. 106 (1977), 38-44. MR0467800 (57:7651)
    • (1977) Ann. of Math. , vol.106 , pp. 38-44
    • Teissier, B.1
  • 29
    • 0040185084 scopus 로고
    • Du theoremedel'index deHodge auxinegalites isoperimetriques
    • MR0524795 (80k:14014)
    • B. Teissier, Du theoremedel'index deHodge auxinegalites isoperimetriques, C.R. Acad. Sci. Paris Ser. A-B 288 (1979), no. 4, A287-A289. MR0524795 (80k:14014)
    • (1979) C.R. Acad. Sci. Paris Ser. A-B , vol.288 , Issue.4
    • Teissier, B.1
  • 30
    • 2542494612 scopus 로고    scopus 로고
    • The Castelnuovo regularity of the Rees algebra and the associated graded ring
    • N.V. Trung, The Castelnuovo regularity of the Rees algebra and the associated graded ring, Trans. Amer. Math. Soc. 350 (1998), 2813-2832. MR1473456 (98j:13006) (Pubitemid 128102479)
    • (1998) Transactions of the American Mathematical Society , vol.350 , Issue.7 , pp. 2813-2832
    • Viet Trung, N.1
  • 31
    • 0035644429 scopus 로고    scopus 로고
    • Positivity of mixed multiplicities
    • DOI 10.1007/s002080000137
    • N.V. Trung, Positivity of mixed multiplicities, Math. Ann. 319 (2001), 33-63. MR1812818 (2001m:13042) (Pubitemid 33726305)
    • (2001) Mathematische Annalen , vol.319 , Issue.1 , pp. 33-63
    • Trung, N.V.1
  • 32
    • 0001387718 scopus 로고
    • Certain graded algebras are always Cohen-Macaulay
    • MR0422249 (54:10240)
    • G. Valla, Certain graded algebras are always Cohen-Macaulay, J. Algebra, 42 (1976), 537-548. MR0422249 (54:10240)
    • (1976) J. Algebra , vol.42 , pp. 537-548
    • Valla, G.1
  • 33
    • 0034347032 scopus 로고    scopus 로고
    • Mixed multiplicities of arbitrary ideals in local rings
    • MR1767591 (2001f:13036)
    • D.Q. Viet, Mixed multiplicities of arbitrary ideals in local rings, Comm. Algebra 28 (8) (2000), 3803-3821. MR1767591 (2001f:13036)
    • (2000) Comm. Algebra , vol.28 , Issue.8 , pp. 3803-3821
    • Viet, D.Q.1
  • 34
    • 0001305505 scopus 로고
    • Rees algebras and mixed multiplicities
    • MR0929432 (89d:13018)
    • J.K. Verma, Rees algebras and mixed multiplicities, Proc. Amer. Math. Soc. 104 (1988), 1036-1044. MR0929432 (89d:13018)
    • (1988) Proc. Amer. Math. Soc. , vol.104 , pp. 1036-1044
    • Verma, J.K.1
  • 35
    • 0001341220 scopus 로고
    • Multigraded Rees algebras and mixed multiplicities
    • MR1149023 (93e:13005)
    • J.K. Verma, Multigraded Rees algebras and mixed multiplicities, J. Pure Appl. Algebra 77 (1992), 219-228. MR1149023 (93e:13005)
    • (1992) J. Pure Appl. Algebra , vol.77 , pp. 219-228
    • Verma, J.K.1
  • 36
    • 0003181588 scopus 로고
    • On Hilbert's function, series of composition of ideals and a generalization of the theorem of Bezout
    • B.L. Van der Waerden, On Hilbert's function, series of composition of ideals and a generalization of the theorem of Bezout, Proc. K. Akad. Wet. Amsterdam 31 (1928), 749-770.
    • (1928) Proc. K. Akad. Wet. Amsterdam , vol.31 , pp. 749-770
    • Waerden Der Van, B.L.1


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