Voir la notice de l'article provenant de la source Cambridge University Press
Kasprzyk, Alexander M. Canonical Toric Fano Threefolds. Canadian journal of mathematics, Tome 62 (2010) no. 6, pp. 1293-1309. doi: 10.4153/CJM-2010-070-3
@article{10_4153_CJM_2010_070_3,
author = {Kasprzyk, Alexander M.},
title = {Canonical {Toric} {Fano} {Threefolds}},
journal = {Canadian journal of mathematics},
pages = {1293--1309},
year = {2010},
volume = {62},
number = {6},
doi = {10.4153/CJM-2010-070-3},
url = {http://geodesic.mathdoc.fr/articles/10.4153/CJM-2010-070-3/}
}
[Bat81] [Bat81] Batyrev, V. V., Toric Fano threefolds. Izv. Akad. Nauk SSSR Ser. Mat. 45(1981), no. 4, 704–717, 927. Google Scholar
[Bat91] [Bat91] Batyrev, V. V., On the classification of smooth projective Toric varieties. Tohoku Math. J. 43(1991), no. 4, 569–585. doi:10.2748/tmj/1178227429 Google Scholar
[Bat94] [Bat94] Batyrev, V. V., Dual polyhedra and mirror symmetry for Calabi-Yau hypersurfaces in toric varieties. J. Algebraic Geom. 3(1994), no. 3, 493–535. Google Scholar
[Bat99] [Bat99] Batyrev, V. V., On the classification of toric Fano 4-folds. J. Math. Sci. (New York) 94(1999), no. 1, 1021–1050. doi:10.1007/BF02367245 Google Scholar
[BB] [BB] Borisov, A. A. and Borisov, L. A., Three-dimensional toric Fano varieties with terminal singularities, unpublished, text in Russian, available upon request. Google Scholar
[BB92] [BB92] Borisov, A. A. and Borisov, L. A., Singular toric Fano three-folds. (Russian) Mat. Sb. 183(1992), no. 2, 134–141, translation in: Russian Acad. Sci. Sb. Math. 75(1993), no. 1, 277–283. Google Scholar
[BB96] [BB96] Batyrev, V. V. and Borisov, L. A., On Calabi-Yau complete intersections in toric varieties. In: Higher-dimensional complex varieties (Trento, 1994), de Gruyter, Berlin, 1996, pp. 39–65. Google Scholar
[Bor00] [Bor00] Borisov, A. A., Convex lattice polytopes and cones with few lattice points inside, from a birational geometry viewpoint. Google Scholar | arXiv
[Bro07] [Bro07] Brown, G., A database of polarized K3 surfaces. Experiment. Math. 16(2007), no. 1, 7–20. Google Scholar
[Con02] [Con02] Conrads, H., Weighted projective spaces and reflexive simplices. Manuscripta Math. 107(2002), no. 2, 215–227. doi:10.1007/s002290100235 Google Scholar
[Cut89] [Cut89] Cutkosky, S. D., On Fano 3-folds. Manuscripta Math. 64(1989), no. 2, 189–204. doi:10.1007/BF01160118 Google Scholar
[Dan78] [Dan78] Danilov, V. I., The geometry of toric varieties. Uspekhi Mat. Nauk 33(1978), no. 2(200), 85–134, 247. Google Scholar
[FS04] [FS04] Fujino, O. and Sato, H., Introduction to the toric Mori theory. Michigan Math. J. 52(2004), no. 3, 649–665. doi:10.1307/mmj/1100623418 Google Scholar
[Ful93] [Ful93] Fulton, W., Introduction to toric varieties. Annals of Mathematics Studies, 131, The William H. Roever Lectures in Geometry, Princeton University Press, Princeton, NJ, 1993. Google Scholar
[Isk79a] [Isk79a] Iskovskih, V. A., Anticanonical models of three-dimensional algebraic varieties. (Russian) Current problems in mathematics, 12, VINITI, Moscow, 1979, pp. 59–157, 239 (loose errata). Google Scholar
[Isk79b] [Isk79b] Iskovskih, V. A., Birational automorphisms of three-dimensional algebraic varieties. (Russian) Current problems in mathematics, 12, VINITI, Moscow, 1979, pp. 159–236, 239 (loose errata). Google Scholar
[Kas06a] [Kas06a] Kasprzyk, A. M., Toric Fano three-folds with terminal singularities. Tohoku Math. J. (2) 58(2006), no. 1, 101–121. doi:10.2748/tmj/1145390208 Google Scholar
[Kas06b] [Kas06b] Kasprzyk, A. M., Toric Fano varieties and convex polytopes, Ph.D. thesis, University of Bath (2006), available from http://hdl.handle.net/10247/458 Google Scholar
[Kas08] [Kas08] Kasprzyk, A. M., Bounds on fake weighted projective space. Kodai Math. J. 32(2009), no. 2, 197–208. doi:10.2996/kmj/1245982903 Google Scholar
[K M M92] [K M M92] Kollár, J., Miyaoka, Y., and Mori, S., Rational connectedness and boundedness of Fano manifolds. J. Differential Geom. 36(1992), no. 3, 765–779. Google Scholar
[KN07] [KN07] Kreuzer, M. and Nill, B., Classification of toric Fano 5-folds. Adv. Geom. 9(2009), no. 1, 85–97. doi:10.1515/ADVGEO M.2009.005 Google Scholar
[KS97] [KS97] Kreuzer, M. and Skarke, H., On the classification of reflexive polyhedra. Comm. Math. Phys. 185(1997), no. 2, 495–508. doi:10.1007/s002200050100 Google Scholar
[KS98] [KS98] Kreuzer, M. and Skarke, H., Classification of reflexive polyhedra in three dimensions. Adv. Theor. Math. Phys. 2(1998), no. 4, 853–871. Google Scholar
[KS00] [KS00] Kreuzer, M. and Skarke, H., Complete classification of reflexive polyhedra in four dimensions. Adv. Theor. Math. Phys. 4(2000), no. 6, 1209–1230. Google Scholar
[KS02] [KS02] Kreuzer, M. and Skarke, H., Reflexive polyhedra, weights and toric Calabi-Yau fibrations. Rev. Math. Phys. 14(2002), no. 4, 343–374. doi:10.1142/S0129055X0200120X Google Scholar
[KS04] [KS04] Kreuzer, M. and Skarke, H., PALP, a package for analyzing lattice polytopes with applications to toric geometry. Computer Phys. Comm. 157(2004), no. 1, 87–106. doi:10.1016/S0010-4655(03)00491-0 Google Scholar
[M M04] [M M04] Mori, S. and Mukai, S., Extremal rays and Fano 3-folds. In: The Fano Conference, Univ. Torino, Turin, 2004, pp. 37–50. Google Scholar
[MU83] [MU83] Mukai, S. and Umemura, H., Minimal rational threefolds. In: Algebraic geometry (Tokyo/Kyoto, 1982), Lecture Notes in Math., 1016, Springer, Berlin, 1983, pp. 490–518. Google Scholar
[Nil05] [Nil05] Nill, B., Gorenstein toric Fano varieties. Manuscripta Math. 116(2005), no. 2, 183–210. doi:10.1007/s00229-004-0532-3 Google Scholar
[Nil06] [Nil06] Nill, B., Classification of pseudo-symmetric simplicial reflexive polytopes. In: Algebraic and geometric combinatorics, Contemp. Math., 423, American Mathematical Society, Providence, RI, 2006, pp. 269–282. Google Scholar
[Øbr07] [Øbr07] Øbro, Mikkel, An algorithm for the classification of smooth Fano polytopes. . Google Scholar | arXiv
[Oda78] [Oda78] Oda, T., Torus embeddings and applications, Tata Institute of Fundamental Research Lectures on Mathematics and Physics, 57, Springer-Verlag, Berlin-New York, 1978. Google Scholar
[Pro05] [Pro05] Prokhorov, Yu. G., The degree of Fano threefolds with canonical Gorenstein singularities. (Russian) Mat. Sb. 196(2005), no. 1, 81–122. Google Scholar
[PRV00] [PRV00] Poonen, B. and F. Rodriguez-Villegas, Lattice polygons and the number 12. Amer. Math. Monthly 107(2000), no. 3, 238–250. doi:10.2307/2589316 Google Scholar
[Rei83] [Rei83] Reid, M., Minimal models of canonical 3-folds. In: Algebraic varieties and analytic varieties, Adv. Stud. Pure Math., 1, North-Holland, Amsterdam, 1983, pp. 131–180. Google Scholar
[Sat00] [Sat00] Sato, Hiroshi, Toward the classification of higher-dimensional toric Fano varieties, Tohoku Math. J. (2) 52(2000), no. 3, 383–413. doi:10.2748/tmj/1178207820 Google Scholar
[Šok79] [Šok79] Šokurov, V. V., The existence of a line on Fano varieties. Izv. Akad. Nauk SSSR Ser. Mat. 43(1979), no. 4, 922–964, 968. Google Scholar
[Tak89] [Tak89] Takeuchi, K., Some birational maps of Fano 3-folds. Compositio Math. 71(1989), no. 3, 265–283. Google Scholar
[Wiś02] [Wiś02] Wiśniewski, J. A., Toric Mori theory and Fano manifolds. In: Geometry of toric varieties, Sémin. Congr., 6, Soc. Math. France, Paris, 2002, pp. 249–272. Google Scholar
[WW82] [WW82] Watanabe, K. and Watanabe, M., The classification of Fano 3-folds with torus embeddings. Tokyo J. Math. 5(1982), no. 1, 37–48. doi:10.3836/tjm/1270215033 Google Scholar
Cité par Sources :