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Asymptotic growth of algebras associated to powers of ideals

  • STEVEN DALE CUTKOSKY (a1), JÜRGEN HERZOG (a2) and HEMA SRINIVASAN (a3)

Abstract

We study generalized symbolic powers and form ideals of powers and compare their growth with the growth of ordinary powers, and we discuss the question of when the graded rings attached to symbolic powers or to form ideals of powers are finitely generated.

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[1]Brodmann, M. and Sharp, R. Y.Local Cohomology: An Algebraic Introduction with Geometric Applications, (Cambridge University Press, 1998).
[2]Bruns, W. and Herzog, J.Cohen–Macaulay Rings. Revised Edition (Cambridge University Press, 1996).
[3]Conca, A., Herzog, J., Trung, N. V. and Valla, G.Diagonal subalgebras of bigraded algebras and embeddings of blow-ups of projective spaces. Amer. J. Math. 119 (1997), 859901.
[4]Cowsik, R. C. and Nori, M. V.On the fibres of blowing up. J. Indian Math. Soc. 40 (1976), 217222.
[5]Cutkosky, S. D.Symbolic algebras of monomial primes. J. Reine Ange. Mathe. 416 (1991), 7189.
[6]Cutkosky, S. D. and Srinivasan, H.An intrinsic criterion for isomorphism of singularities Amer. J. Math. 115 (1993), 789821.
[7]Cutkosky, S. D., Ein, L. and Lazarsfeld, R.Positivity and complexity of ideal sheaves. Math. Ann. 321 (2001), 213234.
[8]Cutkosky, S. D., Ha, H. T., Srinivasan, H. and Theodorescu, E.Asymptotic behaviour of the length of local cohomology. Canad. J. Math. 57 (2005), 11781192.
[9]Cutkosky, S. D., Herzog, J. and Trung, N. V.Asymptotic behaviour of the Castelnuovo–Mumford regularity. Compositio Math. 118 (1999), 243261.
[10]Eisenbud, D. and Goto, S.Linear Free Resolutions and Minimal Multiplicity. J. Algebra 88 (1984), 89133.
[11]Fujita, T.Semipositive line bundles. J. Fac. Sci. Univ. Tokyo 30 (1983), 353378.
[12]Fujita, T.Approximating Zariski decomposition of big line bundles. Kodai Math. J. 17 (1994), 13.
[13]Goto, S., Nishida, K. and Watanabe, K.Non-Cohen-Macaulay symbolic Rees algebras for space monomial curves and counterexamples to Cowsik's question. Proc. Amer. Math. Soc. 120 (1994), 383392.
[14]Herzog, J., Hibi, T. and Trung, N. V.Symbolic powers of monomial ideals and vertex cover algebras. Adv. Math. 210 (2007), 304322.
[15]Herzog, J., Putenpurakal, T. J. and Verma, J. K.Hilbert polynomials and powers of ideals. Math. Proc. Camb. Phil. Soc. 145 (2008), 623642.
[16]Hironaka, H. On the equivalence of singularities, I. Arithmetical Algebraic Geometry, Proceedings, Schilling, O.F.G., ed. (Harper and Row, 1965) 153200.
[17]Huckaba, S.On linear equivalence of the P-adic and P-synbolic topologies. J. Pure Appl. Alg. 46 (1987), 179185.
[18]Hoang, N. D. and Trung, N. V.Hilbert polynomials of non-standard bigraded algebras. Math. Z. 245 (2003), 309334.
[19]Huneke, C.On the finite generation of symbolic blow-ups. Math. Z. 179 (1982), 465472.
[20]Huneke, C. and Swanson, I.Integral closures of ideals, rings and modules. London Math. Society Lecture Note Series 336 (Cambridge University Press, 2006).
[21]Katz, D.Prime divisors, asymptotic R-sequences and unmixed local rings. J. Alg. 95 (1985), 5971.
[22]Katz, D. and Ratliff, L. J.On the symbolic Rees ring of a primary ideal. Comm. Alg. 14 (1986), 959970.
[23]Kirby, D.Hilbert functions and the extension functor. Math. Proc. Camb. Phil. Soc. 105 (1989), 441446.
[24]Kodiyalam, V.Asymptotic behaviour of Castelnuovo-Mumford regularity. Proc. Amer. Math. Soc. 128 (2000), 407411.
[25]Lazarsfeld, R.Positivity in Algebraic Geometry. (Springer Verlag, 2004).
[26]McAdam, S.Asymptotic prime divisors and analytic spreads. Proc. Amer. Math. Soc. 80 (1980), 555559.
[27]Ratliff, L. J.Notes on essentially powers filtrations. Michigan Math. J. 26 (1979), 313324.
[28]Ratliff, L. J.On asymptotic prime divisors. Pacific J. Math. 111 (1984), 395413.
[29]Roberts, P. C.A prime ideal in a polynomial ring whose symbolic blow-up is not Noetherian. Proc. Amer. Math. Soc. 94 (1985), 589592.
[30]Schenzel, P.Finiteness of relative Rees rings and asymptotic prime divisors. Math. Nachr. 129 (1986), 123148.
[31]Theodorescu, E.Derived functors and Hilbert Polynomials. Math. Proc. Camb. Phil. Soc. 132 (2002), 7588.
[32]Ulrich, B. and Validashti, J.A criterion for integral dependence of modules. Math. Res. Lett. 14 (2007), 10411054.
[33]Robbiano, L. and Valla, G.On the equations defining tangent cones. Math. Proc. Camb. Phil. Soc. 88 (1980), 281297.
[34]Verma, J.On ideals whose adic and symbolic topologies are linearly equivalent. J. Pure Appl. Alg. 47 (1987), 205212.
[35]Waldi, R.Vollständige durchschnitte in Cohen–Macaulay-ringen. Arch. Math. 31 (1978), 439442.

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Asymptotic growth of algebras associated to powers of ideals

  • STEVEN DALE CUTKOSKY (a1), JÜRGEN HERZOG (a2) and HEMA SRINIVASAN (a3)

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