The Regularity Conjecture for prime ideals in polynomial rings
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[1] A. Meyer,et al. The complexity of the word problems for commutative semigroups and polynomial ideals , 1982 .
[2] W. Bruns. “Jede” endliche freie auflösung ist freie auflösung eines von drei Elementen erzeugten ideals , 1976 .
[3] Big polynomial rings and Stillman’s conjecture , 2018, Inventiones mathematicae.
[4] André Galligo,et al. Théorème de division et stabilité en géométrie analytique locale , 1979 .
[5] D. Hilbert. Ueber die Theorie der algebraischen Formen , 1890 .
[6] David A. Cox,et al. Ideals, Varieties, and Algorithms: An Introduction to Computational Algebraic Geometry and Commutative Algebra, 3/e (Undergraduate Texts in Mathematics) , 2007 .
[7] M. S. Ravi. Regularity of ideals and their radicals , 1990 .
[8] Castelnuovo–Mumford regularity: examples of curves and surfaces , 2002, math/0210270.
[9] L. Burch. A note on the homology of ideals ǵenerated by three elements in local rings , 1968, Mathematical Proceedings of the Cambridge Philosophical Society.
[10] M. Brodmann,et al. Bounds for the cohomology and the Castelnuovo regularity of certain surfaces , 1993, Nagoya Mathematical Journal.
[11] Joseph Becker. On the boundedness and the unboundedness of the number of generators of ideals and multiplicity , 1977 .
[12] Franz Lemmermeyer,et al. Introduction to Algebraic Geometry , 2005 .
[13] Craig Huneke,et al. Integral closure of ideals, rings, and modules , 2006 .
[14] Hubert Flenner. Die Sätze von Bertini für lokale Ringe , 1977 .
[15] D. Eisenbud. The Geometry of Syzygies: A Second Course in Commutative Algebra and Algebraic Geometry , 2004 .
[16] Jesse Beder,et al. Ideals with larger projective dimension and regularity , 2011, J. Symb. Comput..
[17] D. Hilbert. Über die Theorie der algebraischen Formen , 1890 .
[18] J. McCullough,et al. Counterexamples to the Eisenbud–Goto regularity conjecture , 2017 .
[19] J. Herzog,et al. Castelnuovo–Mumford regularity of simplicial semigroup rings with isolated singularity , 2003 .
[20] Peter Kohn. Ideals generated by three elements , 1972 .
[21] Jinhyung Park,et al. A Castelnuovo-Mumford regularity bound for scrolls , 2016, 1603.02382.
[22] Sijong Kwak. Generic projections, the equations defining projective varieties and Castelnuovo regularity , 2000 .
[23] Sijong Kwak. Castelnuovo regularity for smooth subvarieties of dimensions 3 and 4 , 1998 .
[24] P. Mantero,et al. The projective dimension of codimension two algebra presented by quadrics , 2013, 1304.0745.
[25] S. Lang. Introduction to Algebraic Geometry , 1972 .
[26] Brooke Ullery. Designer ideals with high Castelnuovo-Mumford regularity , 2013, 1305.5966.
[27] W. Vogel,et al. Castelnuovo bounds for certain subvarieties in ℙn , 1987 .
[28] L. Hoa,et al. Bounds on Castelnuovo-Mumford regularity for generalized Cohen-Macaulay graded rings , 1995 .
[29] D. Eisenbud. Commutative Algebra: with a View Toward Algebraic Geometry , 1995 .
[30] Bernd Sturmfels,et al. Syzygies of codimension 2 lattice ideals , 1998 .
[31] M. Stillman,et al. Open Problems on Syzygies and Hilbert Functions , 2009 .
[32] H. Pinkham,et al. A Castelnuovo bound for smooth surfaces , 1986 .
[33] D. Bayer,et al. A criterion for detecting m-regularity , 2008 .
[34] J. McCullough. A family of ideals with few generators in low degree and large projective dimension , 2010, 1005.3361.
[35] Marc Bernd Chardin,et al. Liaison and Castelnuovo-Mumford regularity , 2002 .
[36] David Eisenbud,et al. Linear Free Resolutions and Minimal Multiplicity , 1984 .
[37] A. Bertram,et al. Vanishing theorems, a theorem of Severi, and the equations defining projective varieties , 1991 .
[38] Cohomology of certain projective surfaces with low sectional genus and degree , 1999 .
[39] Z. Ran. Local differential geometry and generic projections of threefolds , 1990 .
[40] Bernd Ulrich,et al. Rational normal scrolls and the defining equations of Rees algebras , 2008, 0812.4963.
[41] C. Huneke. On the Symmetric and Rees Algebra of an Ideal Generated by a d-sequence , 1980 .
[42] Marc Chardin,et al. Bounds for Castelnuovo-Mumford Regularity in Terms of Degrees of Defining Equations , 2003 .
[43] Sijong Kwak. Castelnuovo-Mumford regularity bound for smooth threefolds in ℙ5 and extremal examples , 1999 .
[44] Wenbo Niu. CASTELNUOVO-MUMFORD REGULARITY BOUNDS FOR LOW DIMENSIONAL PROJECTIVE VARIETIES , 2014 .
[45] L. Ein,et al. A vanishing theorem for log canonical pairs , 2008, 0805.3863.
[46] On the Castelnuovo-Mumford regularity of connected curves , 2003, math/0309051.
[47] A. Noma. Generic inner projections of projective varieties and an application to the positivity of double point divisors , 2014 .
[48] Hans Schönemann,et al. SINGULAR: a computer algebra system for polynomial computations , 2001, ACCA.
[49] M. Hochster,et al. Small subalgebras of polynomial rings and Stillman’s Conjecture , 2016, Journal of the American Mathematical Society.
[50] D. Eisenbud,et al. Notes on regularity stabilization , 2012 .
[51] David Mumford,et al. Varieties Defined by Quadratic Equations , 2010 .
[52] M. Hochster,et al. Strength conditions, small subalgebras, and Stillman bounds in degree ≤4 , 2018, 1810.00413.
[53] J. Sidman,et al. A sharp bound for the Castelnuovo–Mumford regularity of subspace arrangements , 2001, math/0109035.
[54] Jinhyung Park,et al. A bound for Castelnuovo-Mumford regularity by double point divisors , 2014, Advances in Mathematics.
[55] Michael Eugene Stillman,et al. On the Complexity of Computing Syzygies , 1988, J. Symb. Comput..
[56] Jee Koh,et al. Ideals Generated by Quadrics Exhibiting Double Exponential Degrees , 1998 .
[57] R. Lazarsfeld. A sharp Castelnuovo bound for smooth surfaces , 1987 .
[58] Marc Giusti,et al. Some Effectivity Problems in Polynomial Ideal Theory , 1984, EUROSAM.
[59] D. Eisenbud,et al. Direct methods for primary decomposition , 1992 .
[60] J. Draisma,et al. Stillman’s conjecture via generic initial ideals , 2018, Communications in Algebra.
[61] P. Mantero,et al. The projective dimension of three cubics is at most 5 , 2018, Journal of Pure and Applied Algebra.
[62] P. Mantero,et al. Singularities of Rees-like algebras , 2019, Mathematische Zeitschrift.
[63] M. Chardin,et al. Regularity of prime ideals , 2018, Mathematische Zeitschrift.
[64] David Mumford,et al. Lectures on curves on an algebraic surface , 1966 .
[65] G. Castelnuovo. Sui multipli di una serie lineare di gruppi di punti appartenente ad una curva algebrica , 1893 .
[66] Steven V. Sam,et al. Cubics in 10 variables vs. cubics in 1000 variables: Uniformity phenomena for bounded degree polynomials , 2018, Bulletin of the American Mathematical Society.
[67] D. Eisenbud,et al. Lectures on the Geometry of Syzygies , 2005 .
[68] Giulio Caviglia,et al. Characteristic-free bounds for the Castelnuovo–Mumford regularity , 2005, Compositio Mathematica.
[69] David Mumford,et al. What Can Be Computed in Algebraic Geometry , 1993, alg-geom/9304003.