Tamagawa numbers of polarized algebraic varieties
Nombre et répartition de points de hauteur bornée, Astérisque no. 251  (1998), p. 299-340
@incollection{AST_1998__251__299_0,
     author = {Batyrev, Victor V. and Tschinkel, Yuri},
     title = {Tamagawa numbers of polarized algebraic varieties},
     booktitle = {Nombre et r\'epartition de points de hauteur born\'ee},
     editor = {Peyre Emmanuel},
     series = {Ast\'erisque},
     publisher = {Soci\'et\'e math\'ematique de France},
     number = {251},
     year = {1998},
     pages = {299-340},
     zbl = {0926.11045},
     mrnumber = {1679843},
     language = {en},
     url = {http://www.numdam.org/item/AST_1998__251__299_0}
}
Batyrev, Victor V.; Tschinkel, Yuri. Tamagawa numbers of polarized algebraic varieties, in Nombre et répartition de points de hauteur bornée, Astérisque, no. 251 (1998), pp. 299-340. http://www.numdam.org/item/AST_1998__251__299_0/

[1] D. Abramovich, J. Wang, Equivariant resolution of singularities in characteristic 0, alg-geom/9609013. | Article | Zbl 0906.14005

[2] V. Alekseev, Fractional indices of log del Pezzo surfaces, Math. USSR, Izvestia, 33 (1989), 613-629. | Article | MR 984220 | Zbl 0724.14023

[3] S. J. Arakelov, Theory of intersections on the arithmetic surface, in Proceedings of the International Congress of Math., Vol. 1, Canad. Math. Congress, Montreal, (1975), 405-408. | MR 466150 | Zbl 0351.14003

[4] V. Batyrev, Yu. I. Manin, Sur le nombre des points rationnels de hauteur bornée des variétés algébriques, Math. Ann., 286, (1990), 27-43. | Article | MR 1032922 | Zbl 0679.14008

[5] V. Batyrev, The cone of effective divisors of threefolds, Proc. Mal'cev Conference, Contemporary Mathematics, 131, Part 3 (1992), 337-352. | MR 1175891 | Zbl 0781.14027

[6] V. Batyrev, Yu. Tschinkel, Rational points of bounded height on compactifications of anisotropic tori, Intern. Math. Research Notices, 12, (1995), 591-635. | Article | MR 1369408 | Zbl 0890.14008

[7] V. Batyrev, Yu. Tschinkel, Manin's conjecture for toric varieties, Journal of Alg. Geometry, 7 (1998), 15-53. | MR 1620682 | Zbl 0946.14009

[8] V. Batyrev, Yu. Tschinkel, Height zeta functions of toric varieties, Algebraic geometry, 5, (Manin's Festschrift), J. Math. Sci., 82, no. 1, (1996), 3220-3239. | MR 1423638 | Zbl 0915.14013

[9] V. Batyrev, Yu. Tschinkel, Rational points on some Fano cubic bundles, C. R. Acad. Sci., Paris, 323, Ser. I, (1996), 41-46. | MR 1401626 | Zbl 0879.14007

[10] A. Borel, Linear algebraic groups, New York-Amsterdam, (1969). | MR 251042 | Zbl 0726.20030 | Zbl 0186.33201

[11] J. L. Brylinski, Décomposition simpliciale d'un réseau, invariante par un groupe fini d'automorphismes, C. R. Acad. Sci., Paris, Sér. A-B, 288, (1979), A137-A139. | MR 524769 | Zbl 0406.14022

[12] D. Cox, Recent developments in toric geometry, alg-geom 9606016. | Zbl 0899.14025

[13] V. I. Danilov, The geometry of toric varieties, Russ. Math. Surveys, 33, (1978), n. 2, 97-154. | Article | MR 495499 | Zbl 0425.14013

[14] H. Delange, Généralisation du théorème de Ikehara, Ann. Sci. Ecole Norm. Sup., (4), 71, (1954), 213-242. | Article | Numdam | MR 68667 | Zbl 0056.33101

[15] P. Deligne, La conjecture de Weil I, Inst. Hautes Études Sci. Publ. Math., 43, (1973), 273-307. | Article | Numdam | MR 340258 | Zbl 0287.14001

[16] J. Denef, On the degree of Igusa's local zeta function, Amer. J. Math., 109, (1987), 991-1008. | Article | MR 919001 | Zbl 0659.14017

[17] G. Faltings, Calculus on arithmetic surfaces, Ann. of Math., (2), 119, (1984), 387-424. | Article | MR 740897 | Zbl 0559.14005

[18] E. Fouvry, Sur la hauteur de points d'une certaine surface cubique singulière, this volume, (1996). | Zbl 0930.11044

[19] J. Franke, Yu. I. Manin, Yu. Tschinkel, Rational points of bounded height on Fano varieties, Inventiones Math., 95, (1989), p. 421-435. | Article | MR 974910 | Zbl 0674.14012

[20] T. Fujita, On Kodaira energy and adjoint reduction of polarized manifolds, Manuscripta Math., 76, (1992), 59-84. | Article | MR 1171156 | Zbl 0766.14027

[21] T. Fujita, Notes on Kodaira energies of polarized varieties, Preprint, alg-geom/9205004.

[22] T. Fujita, Kodaira energies of polarized log varieties, Preprint, alg-geom/9305004. | Article | Zbl 0914.14001

[23] T. Fujita, On Kodaira energy of polarized log varieties, J. Math. Soc. Japan, 48-1, (1996), 1-12. | Article | MR 1361544 | Zbl 0914.14001

[24] T. Fujita, On Kodaira energy and adjoint reduction of polarized threefolds, alg-geom/9611031. | Article | Zbl 0969.14001

[25] W. Fulton, Introduction to toric varieties, Princeton U. Press, Princeton, (1993). | MR 1234037 | Zbl 0813.14039

[26] H. Hironaka, Resolution of singularities of an algebraic variety over a field of characteristic zero, Ann. Math., 79, (1964), 109-326. | Article | MR 199184 | Zbl 0122.38603

[27] Y. Kawamata, K. Matsuda and K. Matsuki, Introduction to the Minimal Model Program, Adv. Studies in Pure Math., 10, (1987), 283-360. | Article | MR 946243 | Zbl 0672.14006

[28] Y. Kawamata, Boundedness of 𝐐 - F a n o 3 -folds, Contemp. Math., 131, (1992), 439-445. | MR 1175897 | Zbl 0785.14024

[29] S. Lang, Fundamentals of Diophantine Geometry, Springer-Verlag, New York-Berlin-Heidelberg-Tokyo, (1983). | Article | MR 715605 | Zbl 0528.14013

[30] E. Peyre, Hauteurs et nombres de Tamagawa sur les variétés de Fano, Duke Math. J., 79, (1995), 101-218. | MR 1340296 | Zbl 0901.14025

[31] S. Schanuel, Heights in number fields, Bull. Soc. Math. France, 107 (1979), 433-449. | Article | Numdam | MR 557080 | Zbl 0428.12009

[32] K.-H. Shin, 3-dimensional Fano varieties with canonical singularities, Tokyo J. Math., 12, (1989), 375-385. | Article | MR 1030501 | Zbl 0708.14025

[33] M. Strauch, Yu. Tschinkel, Height zeta functions of twisted products, Math. Res. Letters, 4, (1997), 273-282. | Article | MR 1453059 | Zbl 0918.11036

[34] R. C. Vaugan, T. D. Wooley, On a certain nonary cubic form and related equations, Duke Math. J., 80, (1995), 669-735. | Article | MR 1370112 | Zbl 0847.11052

[35] A. Weil, Adèles and algebraic groups, Progr. Math., 23, Birkhäuser, Boston (1982). | MR 670072 | Zbl 0493.14028