References
- Albert, M., Fetzer, M., Sáenz-de Cabezón, E., Seiler, W. M. (2015). On the free resolution induced by a Pommaret basis. J. Symbolic Comput. 68(2):4–26. DOI: 10.1016/j.jsc.2014.09.008.
- Bayer, D. A. (1982). The division algorithm and the Hilbert scheme. Thesis (Ph.D.)–Harvard University. ProQuest LLC, Ann Arbor, MI.
- Bertone, C. (2015). Quasi-stable ideals and Borel-fixed ideals with a given Hilbert polynomial. Appl. Algebra Eng. Commun. Comput. 26(6):507–525.
- Bruns, W., Herzog, J. (1993). Cohen-Macaulay Rings. Cambridge Studies in Advanced Mathematics, Vol. 39. Cambridge: Cambridge University Press.
- Bayer, D., Stillman, M. (1987). A criterion for detecting m-regularity. Invent. Math. 87(1):1–11.
- Bayer, D., Stillman, M. (1987). A theorem on refining division orders by the reverse lexicographic order. Duke Math. J. 55(2):321–328.
- Cioffi, F., Lella, P., Marinari, M. G., Roggero, M. (2011). Segments and Hilbert schemes of points. Discrete Math. 311(20):2238–2252.
- Ellia, P., Hirschowitz, A., Mezzetti, E. (1992). On the number of irreducible components of the Hilbert scheme of smooth space curves. Int. J. Math. 3(6):799–807.
- Eisenbud, D. (1995). Commutative Algebra, Graduate Texts in Mathematics, Vol. 150. New York: Springer-Verlag, With a view toward algebraic geometry.
- Eisenbud, D. (2005). The Geometry of Syzygies, Graduate Texts in Mathematics, Vol. 229. New York: Springer-Verlag, A second course in commutative algebra and algebraic geometry.
- Eliahou, S., Kervaire, M. (1990). Minimal resolutions of some monomial ideals. J. Algebra 129(1):1–25. DOI: 10.1016/0021-8693(90)90237-I.
- Francisco, C. A., Mermin, J., Schweig, J. (2011). Borel generators. J. Algebra 332:522–542. DOI: 10.1016/j.jalgebra.2010.09.042.
- Fogarty, J. (1968). Algebraic families on an algebraic surface. Am. J. Math. 90:511–521. DOI: 10.2307/2373541.
- Fogarty, J. (1973). Fixed point schemes. Am. J. Math. 95:35–51. DOI: 10.2307/2373642.
- Gotzmann, G. (1978). Eine Bedingung für die Flachheit und das Hilbertpolynom eines graduierten Ringes. Math. Z. 158(1):61–70.
- Grayson, D. R., Stillman, M. E. Macaulay2, a software system for research in algebraic geometry. http://www.math.uiuc.edu/Macaulay2/.
- Hartshorne, R. (1966). Connectedness of the Hilbert scheme. Inst. Hautes Études Sci. Publ. Math. 29:5–48.
- Herzog, J., Hibi, T. (2011). Monomial Ideals, Graduate Texts in Mathematics, Vol. 260. London: Springer-Verlag.
- Herzog, J., Popescu, D. (2001). On the regularity of p-Borel ideals. Proc. Am. Math. Soc. 129(9):2563–2570.
- Iarrobino, A. (1972). Reducibility of the families of 0-dimensional schemes on a variety. Invent. Math. 15:72–77. DOI: 10.1007/BF01418644.
- Iarrobino, A., Kanev, V. (1999). Power Sums, Gorenstein Algebras, and Determinantal Loci, Lecture Notes in Mathematics, Vol. 1721. Berlin: Springer-Verlag, Appendix C by Iarrobino and Steven L. Kleiman.
- Macaulay, F. S. (1927). Some properties of enumeration in the theory of modular systems. Proc. London Math. Soc. S2–26(1):531.
- Moore, D., Nagel, U. (2014). Algorithms for strongly stable ideals. Math. Comp. 83(289):2527–2552.
- Miller, E., Sturmfels, B. (2005). Combinatorial Commutative Algebra, Graduate Texts in Mathematics, Vol. 227. New York: Springer-Verlag.
- Mumford, D. (1962). Further pathologies in algebraic geometry. Am. J. Math. 84:642–648. DOI: 10.2307/2372870.
- Notari, R., Spreafico, M. L. (2000). A stratification of Hilbert schemes by initial ideals and applications. Manuscripta Math. 101(4):429–448.
- Pardue, K. (1994). Nonstandard borel-fixed ideals. ProQuest LLC, Ann Arbor, MI, 1994, Thesis (Ph.D.)–Brandeis University.
- Pardue, K. (1996). Deformation classes of graded modules and maximal Betti numbers. Illinois J. Math. 40(4):564–585.
- Peeva, I. (2011). Graded Syzygies, Algebra and Applications, Vol. 14. London: Springer-Verlag.
- Piene, R., Schlessinger, M. (1985). On the Hilbert scheme compactification of the space of twisted cubics. Am. J. Math. 107(4):761–774.
- Peeva, I., Stillman, M. (2005). Connectedness of Hilbert schemes. J. Algebraic Geom. 14(2):193–211. DOI: 10.1090/S1056-3911-04-00386-8.
- Ramkumar, R. (2023). Hilbert schemes with two borel-fixed points. J. Algebra 617:17–47. DOI: 10.1016/j.jalgebra.2022.11.003.
- Reeves, A. A. (1992). Combinatorial structure on the Hilbert scheme. Thesis (Ph.D.)–Cornell University. ProQuest LLC, Ann Arbor, MI.
- Reeves, A. A. (1995). The radius of the Hilbert scheme. J. Algebraic Geom. 4()4:639–657.
- Reeves, A., Stillman, M. (1997). Smoothness of the lexicographic point. J. Algebraic Geom. 6(2):235–246.
- Seiler, W. M. (2009). A combinatorial approach to involution and δ-regularity. II. Structure analysis of polynomial modules with Pommaret bases. Appl. Algebra Eng. Commun. Comput. 20(3–4):261–338.
- Skjelnes, R., Smith, G. G. (2023). Smooth Hilbert schemes: Their classification and geometry. J. für Reine Angew. Math. (Crelles Journal) 2023(794):281–305.
- Staal, A. P. (2020). The ubiquity of smooth Hilbert schemes. Math. Z. 296(3–4):1593–1611.
- Synefakopoulos, A. (2007). On some classes of borel fixed ideals and their cellular resolutions. Thesis (Ph.D.)–Cornell University. ProQuest LLC, Ann Arbor, MI.
- Vakil, R. (2006). Murphy’s law in algebraic geometry: badly-behaved deformation spaces. Invent. Math. 164(3):569–590.