Tamagawa numbers of polarized algebraic varieties
Nombre et répartition de points de hauteur bornée, Astérisque, no. 251 (1998), pp. 299-340.
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     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},
     pages = {299--340},
     publisher = {Soci\'et\'e math\'ematique de France},
     number = {251},
     year = {1998},
     mrnumber = {1679843},
     zbl = {0926.11045},
     language = {en},
     url = {http://archive.numdam.org/item/AST_1998__251__299_0/}
}
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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://archive.numdam.org/item/AST_1998__251__299_0/

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

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

[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 | Zbl

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

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

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

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

[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 | Zbl

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

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

[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 | Zbl

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

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

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

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

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

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

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

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

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

[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. | DOI | Zbl

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

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

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

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

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

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

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

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

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

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

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

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

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