Abstract
In this paper we compute the minimal free resolution and then the Hilbert function of a \(m\)-homogeneous fat complete grid in \(\mathbb {P}^3_\mathbf {K}\). This proves a conjecture about the minimal free resolution of these configurations of lines.
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Eisenbud, D.: The geometry of syzygies. J. Pure Appl. Algebra 208(2), 603–615 (2007)
Francisco, C.A., Migliore, J., Nagel, U.: On the componentwise linearity and the minimal free resolution of a tetrahedral curve. J. Algebra 299(2), 535–569 (2006)
Francisco, C.A.: Resolution of small sets of fat points. J. Pure Appl. Algebra 203(1–3), 220–236 (2005)
Guida, M., Orecchia, F.: Algebraic properties of grids of projective lines. J. Pure Appl. Algebra 208(2), 603–615 (2007)
Guida, M., Orecchia, F.: Algebraic properties of grids of fat lines. Int. J. Pure Appl. Math. 40(4), 519–542 (2007)
Guida, M.: Syzygies of grids of projective lines. Ricerche mat. 57, 159–167 (2008)
Migliore, J.: Introduction to Liaison Theory and Deficiency Modules, Progress in Mathematics, vol.165. Birkhäuser Boston Inc., Boston, MA (1998)
Migliore, J., Nagel, U.: Tetrahedral Curves. Int. Math. Res. Not. 15, 899–939 (2005)
Miller, E., Sturmfels, B., Yanagawa, K.: Generic and cogeneric monomial ideals, Symbolic computation in algebra, analysis, and geometry (Berkeley, CA, 1998). J. Symbolic Comput. 29(4–5), 691–708 (2000)
Mora, T.: Solving Polynomial Equation Systems II: Macaulay’s Paradigm and Gröbner Technology, Encyclopedia of Mathematics and Its Applications 99. Cambridge University Press, Cambridge (2005)
Valla, G.: Betti numbers of some monomial ideals. Proc. Am. Math. Soc. 133, 57–63 (2005)
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Guida, M. Minimal free resolutions of some configurations of fat lines. AAECC 25, 297–310 (2014). https://doi.org/10.1007/s00200-014-0229-0
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DOI: https://doi.org/10.1007/s00200-014-0229-0