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Original Articles

Non-Normal Very Ample Polytopes – Constructions and Examples

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References

  • [Beck et al. 15] M. Beck, J. Delgado, J. Gubeladze, and M. Michałek. “Very Ample and Koszul Segmental Fibrations.” J. Algebraic Comb. 42:1 (2015), 165–182.
  • [Bruns and Gubeladze 02] W. Bruns and J. Gubeladze. “Semigroup Algebras and Discrete Geometry.” In Geometry of Toric Varieties, Sémin. Congr., vol. 6, edited by L. Bonavero and M. Brion, pp. 43–127. Paris: Soc. Math. France, 2002.
  • [Bruns and Gubeladze 04] W. Bruns and J. Gubeladze. “Polytopes and K-Theory.” Georgian Math. J. 11:4 (2004), 655–670.
  • [Bruns et al. 15] W. Bruns, J. Gubeladze, and M. Michałek. “Quantum Jumps of Normal Polytopes.” arXiv:1504.01036.
  • [Bruns et al.] W. Bruns, B. Ichim, T. Römer, and C. Söger. Normaliz. Computing normalizations of affine semigroups. Available from http://www.math.uos.de/normaliz
  • [Bruns 13] W. Bruns. “The Quest for Counterexamples in Toric Geometry.” In Commutative Algebra and Algebraic Geometry, Ramanujan Math. Soc. Lect. Notes Ser., vol. 17, edited by H. Flenner, and D. Patil, pp. 45–61. Mysore: Ramanujan Math. Soc., 2013. Available online http://www.home.uni-osnabrueck.de/wbruns/brunsw/pdf-article/2-quest-WB.pdf
  • [Cox et al. 11] D. A. Cox, J. B. Little, and H. K. Schenck. Toric Varieties, Graduate Studies in Mathematics, vol. 124. Providence, RI: American Mathematical Society, 2011.
  • [Cox et al. 14] D. A. Cox, C. Hasse, T. Hibi, and A. Higashitani. “Integer Decomposition Property of Dilated Polytopes.” Electr. J. Comb. 21:4 (2014), 4–28.
  • [Decker et al. 12] W. Decker, G.-M. Greuel, G. Pfister, and H. Schönemann. “Singular 3-1-6 – A Computer Algebra System for Polynomial Computations.” Available online (http://www.singular.uni-kl.de), 2012.
  • [Ehrhart 62] E. Ehrhart. “Sur les polyédres homothétiques bordés á n Dimensions.” C. R. Acad. Sci. Paris 254 (1962), 988–990.
  • [Fulton 93] W. Fulton. Introduction to Toric Varieties, Annals of Mathematics Studies, vol. 131. Princeton, NJThe William H. Roever Lectures in Geometry, Princeton University Press, 1993.
  • [Gawrilow and Joswig 00] E. Gawrilow and M. Joswig. “Polymake: A Framework for Analyzing Convex Polytopes.” In Polytopes, combinatorics and computation (Oberwolfach, 1997), DMV Sem., vol. 29, pp. 43–73. Basel: Birkhäuser, 2000.
  • [Gelfand et al. 87] I. Gelfand, M. Goresky, R. MacPherson, and V. Serganova. “Combinatorial Geometries, Convex Polyhedra, and Schubert Cells.” Adv. Math. 63:3 (1987), 301–316.
  • [Hasse et al. 07] C. Hasse, T. Hibi, and D. Maclagan. “Mini-Workshop: Projective Normality of Smooth Toric Varieties.” Oberwolfach Rep. 4:3 (2007), 2283–2320.
  • [Haase et al. 14] C. Haase, A. Paffenholz, L. Piechnik, and F. Santos. “Existence of Unimodular Triangulations-Positive Results.” arXiv:1405.1687, 2014.
  • [Higashitani 14] A. Higashitani. “Non-Normal Very Ample Polytopes and Their Holes.” Electr. J. Comb. 21:1 (2014), 1–53.
  • [Kahle and Michałek to appear] T. Kahle and M. Michałek. “Plethysm and Lattice Point Counting.” To appear in Found. Comput. Math. doi:10.1007/s10208-015-9275-7
  • [Lasoń and Michałek 14] M. Lasoń and M. Michałek. “On the Toric Ideal of a Matroid.” Adv. Math. 259 (2014), 1–12.
  • [Michałek 15] M. Michałek. “Toric Varieties in Phylogenetics.” Dissertationes Mathematicae 511 (2015), 1–86.
  • [Nakajima 86] H. Nakajima. “Affine Torus Embeddings which are Complete Intersections.” Tohoku Math. J. 38:1 (1986), 85–98.
  • [Ogata 13] S. Ogata. “Very Ample But Not Normal Lattice Polytopes.” Beiträge zur Algebra und Geometrie/Contrib. Algebra Geom. 54:1 (2013), 291–302.
  • [Ohsugi and Hibi 98] H. Ohsugi and T. Hibi. “Normal Polytopes Arising from Finite Graphs.” J. Algebra 207:2 (1998), 409–426.
  • [Ohsugi and Hibi 99] H. Ohsugi and T. Hibi. “Toric Ideals Generated by Quadratic Binomials.” J. Algebra 218:2 (1999), 509–527.
  • [Ohsugi and Hibi 01] H. Ohsugi and T. Hibi. “Convex Polytopes All of Whose Reverse Lexicographic Initial Ideals are Squarefree.” Proc. Am. Math. Soc. 129:9 (2001), 2541–2546.
  • [Ohsugi et al. 00] H. Ohsugi, J. Herzog, and T. Hibi. “Combinatorial Pure Subrings.” Osaka J. Math. 37:3 (2000), 745–757.
  • [Stanley 86] R. Stanley. “Two Poset Polytopes.” Discrete Comput. Geom. 1:1 (1986), 9–23.
  • [Sturmfels 96] B. Sturmfels. Gröbner Bases and Convex Polytopes, University Lecture Series, vol. 8. Providence, RI: American Mathematical Society, 1996.
  • [Sturmfels and Sullivant 05] B. Sturmfels and S. Sullivant. “Toric Ideals of Phylogenetic Invariants.” J. Comput. Biol. 12:2 (2005), 204–228.
  • [Sullivant 06] S. Sullivant. “Compressed Polytopes and Statistical Disclosure Limitation.” Tohoku Math. J. (2) 58:3 (2006), 433–445.

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