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Original Articles

Four-Dimensional Projective Orbifold Hypersurfaces

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References

  • [Bosma et al. 97] Wieb Bosma, John Cannon, and Catherine Playoust. “The Magma Algebra System. I. The User Language.” J. Symbolic Comput. 24:3–4 (1997), 235–265. Computational algebra and number theory (London, 1993).
  • [Boyer et al. 03] Charles P. Boyer, Krzysztof Galicki, and Michael Nakamaye. “Sasakian Geometry, Homotopy Spheres and Positive Ricci Curvature.” Topology 42:5 (2003), 981–1002.
  • [Brown and Kasprzyk 02] Gavin Brown and Alexander M. Kasprzyk. “The Graded Ring Database.” Available at http://www.grdb.co.uk/, 2002.
  • [Brown and Suzuki 07] Gavin Brown and Kaori Suzuki. “Computing Certain Fano 3-Folds.” Jpn. J. Ind. Appl. Math. 24:3 (2007), 241–250.
  • [Cheltsov and Park 13] Ivan Cheltsov and Jihun Park. “Birationally Rigid Fano Threefold Hypersurfaces.” arXiv:1309.0903 [math.AG], 2013.
  • [Cheltsov et al. 10] Ivan Cheltsov, Jihun Park, and Constantin Shramov. “Exceptional del Pezzo Hypersurfaces.” J. Geom. Anal. 20:4 (2010), 787–816.
  • [Cheltsov and Shramov 13] Ivan Cheltsov and Constantin Shramov. “Del Pezzo Zoo.” Exp. Math. 22:3 (2013), 313–326.
  • [Chen and Chen 14] Jungkai A. Chen and Meng Chen. “Explicit Birational Geometry of 3-Folds and 4-Folds of General Type, III.” Comp. Math. 151:6, (2014), 1041–1082.
  • [Corti et al. 00] Alessio Corti, Aleksandr Pukhlikov, and Miles Reid. “Fano 3-Fold Hypersurfaces.” In A. Corti and M. Reid (eds.) Explicit Birational Geometry of 3-Folds, Volume 281 of London Math. Soc. Lecture Note Ser., pp. 175–258. Cambridge: Cambridge University Press, 2000.
  • [Dolgachev 82] Igor Dolgachev. “Weighted Projective Varieties.” In J. B. Carrell (ed.) Group Actions and Vector Fields (Vancouver, BC, 1981), Volume 956 of Lecture Notes in Math., pp. 34–71. Berlin: Springer, 1982.
  • [Iano-Fletcher 00] A. R. Iano-Fletcher. “Working with Weighted Complete Intersections.” In A. Corti and M. Reid (eds.) Explicit Birational Geometry of 3-Folds, Volume 281 of London Math. Soc. Lecture Note Ser., pp. 101–173. Cambridge: Cambridge University Press, 2000.
  • [Johnson and Kollár 01a] J. M. Johnson and J. Kollár. “Kähler-Einstein Metrics on Log del Pezzo Surfaces in Weighted Projective 3-Spaces.” Ann. Inst. Fourier (Grenoble) 51:1 (2001), 69–79.
  • [Johnson and Kollár 01b] Jennifer M. Johnson and János Kollár. “Fano Hypersurfaces in Weighted Projective 4-Spaces.” Exp. Math. 10:1 (2001), 151–158.
  • [Kasprzyk 13] Alexander M. Kasprzyk. “Classifying Terminal Weighted Projective Space.” arXiv:1304.3029 [math.AG], 2013.
  • [Keel and McKernan 99] Seán Keel and James McKernan. “Rational Curves on Quasi-Projective Surfaces.” Mem. Amer. Math. Soc. 140:669 (1999), viii+153.
  • [Kreuzer and Skarke 02] Maximilian Kreuzer and Harald Skarke. “Calabi–Yau Data and PALP Webpage.” Available at http://hep.itp.tuwien.ac.at/∼kreuzer/CY/, 2002.
  • [Kreuzer and Skarke 00] Maximilian Kreuzer and Harald Skarke. “Complete Classification of Reflexive Polyhedra in Four Dimensions.” Adv. Theor. Math. Phys. 4:6 (2000), 1209–1230.
  • [Paemurru 13] Erik Paemurru. “Del Pezzo Surfaces in Weighted Projective Spaces.” arXiv:1301.5430 [math.AG], 2013.
  • [Prokhorov 10] Yuri Prokhorov. “-Fano Threefolds of Large Fano Index, I.” Doc. Math. 15 (2010), 843–872.
  • [Reid 80] Miles Reid. “Canonical 3-Folds.” In A. Beauville (ed.) Journées de Géometrie Algébrique d’Angers, Juillet 1979/Algebraic Geometry, Angers, 1979, pp. 273–310. Alphen aan den Rijn: Sijthoff & Noordhoff, 1980.
  • [Reid 87] Miles Reid. “Young Person’s Guide to Canonical Singularities.” In S. J. Bloch (ed.) Algebraic Geometry, Bowdoin, 1985 (Brunswick, Maine, 1985), Volume 46 of Proc. Sympos. Pure Math., pp. 345–414. Providence, RI: American Mathematical Society, 1987.
  • [Suzuki 04] Kaori Suzuki. “On Fano Indices of -Fano 3-Folds.” Manuscr. Math. 114:2 (2004), 229–246.
  • [Tai 82] Yung-Sheng Tai. “On the Kodaira Dimension of the Moduli Space of Abelian Varieties.” Invent. Math. 68:3 (1982), 425–439.
  • [Yau and Yu 05] Stephen S.-T. Yau and Yung Yu. “Classification of 3-Dimensional Isolated Rational Hypersurface Singularities with C*-Action.” Rocky Mountain J. Math. 35:5 (2005), 1795–1809.

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