Uniformity of rational points
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- by Lucia Caporaso, Joe Harris and Barry Mazur
- J. Amer. Math. Soc. 10 (1997), 1-35
- DOI: https://doi.org/10.1090/S0894-0347-97-00195-1
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References
- D.Abramovich. On the number of stably integral points on an elliptic curve. preprint.
- D.Abramovich. Uniformité des points rationnels des courbes algébriques sur les extensions quadratiques et cubiques. preprint.
- Dan Abramovich and Joe Harris, Abelian varieties and curves in $W_d(C)$, Compositio Math. 78 (1991), no. 2, 227â238. MR 1104789
- S. Ju. Arakelov, Families of algebraic curves with fixed degeneracies, Izv. Akad. Nauk SSSR Ser. Mat. 35 (1971), 1269â1293 (Russian). MR 0321933
- E. Arbarello, M. Cornalba, P. A. Griffiths, and J. Harris, Geometry of algebraic curves. Vol. I, Grundlehren der mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences], vol. 267, Springer-Verlag, New York, 1985. MR 770932, DOI 10.1007/978-1-4757-5323-3
- Edward Bierstone and Pierre D. Milman, A simple constructive proof of canonical resolution of singularities, Effective methods in algebraic geometry (Castiglioncello, 1990) Progr. Math., vol. 94, BirkhĂ€user Boston, Boston, MA, 1991, pp. 11â30. MR 1106412, DOI 10.1007/978-1-4612-0441-1_{2}
- F. A. Bogomolov, Families of curves on a surface of general type, Dokl. Akad. Nauk SSSR 236 (1977), no. 5, 1041â1044 (Russian). MR 0457450
- L.Caporaso, J.Harris, B.Mazur. How many rational points can a curve have? Proceedings of the Texel Conference, Progress in Math. vol. 129, Birkhauser Boston, 1995, p. 13â31.
- L.Caporaso, J.Harris, B.Mazur. Uniformity of rational points. Preliminary version of this paper, available by anonymous ftp from math.harvard.edu.
- Schémas en groupes. I: Propriétés générales des schémas en groupes, Lecture Notes in Mathematics, Vol. 151, Springer-Verlag, Berlin-New York, 1970 (French). Séminaire de Géométrie Algébrique du Bois Marie 1962/64 (SGA 3); Dirigé par M. Demazure et A. Grothendieck. MR 0274458
- Lawrence Ein, Subvarieties of generic complete intersections. II, Math. Ann. 289 (1991), no. 3, 465â471. MR 1096182, DOI 10.1007/BF01446583
- RenĂ©e Elkik, SingularitĂ©s rationnelles et dĂ©formations, Invent. Math. 47 (1978), no. 2, 139â147 (French). MR 501926, DOI 10.1007/BF01578068
- Gerd Faltings, The general case of S. Langâs conjecture, Barsotti Symposium in Algebraic Geometry (Abano Terme, 1991) Perspect. Math., vol. 15, Academic Press, San Diego, CA, 1994, pp. 175â182. MR 1307396
- Peter Scherk, Bemerkungen zu einer Note von Besicovitch, J. London Math. Soc. 14 (1939), 185â192 (German). MR 29, DOI 10.1112/jlms/s1-14.3.185
- Robin Hartshorne, Ample subvarieties of algebraic varieties, Lecture Notes in Mathematics, Vol. 156, Springer-Verlag, Berlin-New York, 1970. Notes written in collaboration with C. Musili. MR 0282977, DOI 10.1007/BFb0067839
- B.Hassett. Correlation for surfaces of general type. preprint.
- Heisuke Hironaka, Idealistic exponents of singularity, Algebraic geometry (J. J. Sylvester Sympos., Johns Hopkins Univ., Baltimore, Md., 1976) Johns Hopkins Univ. Press, Baltimore, Md., 1977, pp. 52â125. MR 0498562
- JĂĄnos KollĂĄr, Subadditivity of the Kodaira dimension: fibers of general type, Algebraic geometry, Sendai, 1985, Adv. Stud. Pure Math., vol. 10, North-Holland, Amsterdam, 1987, pp. 361â398. MR 946244, DOI 10.2969/aspm/01010361
- JĂĄnos KollĂĄr, Projectivity of complete moduli, J. Differential Geom. 32 (1990), no. 1, 235â268. MR 1064874
- Serge Lang, Hyperbolic and Diophantine analysis, Bull. Amer. Math. Soc. (N.S.) 14 (1986), no. 2, 159â205. MR 828820, DOI 10.1090/S0273-0979-1986-15426-1
- E.Looijenga. Smooth Deligne-Mumford compactifications by means of Prym levels structires. J.AlgGeom. 3 (1992) p.283-293.
- S.Lu, M. Miyaoka. preprint.
- David Mumford, Stability of projective varieties, Enseign. Math. (2) 23 (1977), no. 1-2, 39â110. MR 450272
- David Mumford and John Fogarty, Geometric invariant theory, 2nd ed., Ergebnisse der Mathematik und ihrer Grenzgebiete [Results in Mathematics and Related Areas], vol. 34, Springer-Verlag, Berlin, 1982. MR 719371, DOI 10.1007/978-3-642-96676-7
- Herbert Popp, ModulrĂ€ume algebraischer Mannigfaltigkeiten, Classification of algebraic varieties and compact complex manifolds, Lecture Notes in Math., Vol. 412, Springer, Berlin, 1974, pp. 219â242 (German). MR 0360581
- Herbert Popp, Moduli theory and classification theory of algebraic varieties, Lecture Notes in Mathematics, Vol. 620, Springer-Verlag, Berlin-New York, 1977. MR 0466143, DOI 10.1007/BFb0067436
- Miles Reid, Canonical $3$-folds, JournĂ©es de GĂ©ometrie AlgĂ©brique dâAngers, Juillet 1979/Algebraic Geometry, Angers, 1979, Sijthoff & Noordhoff, Alphen aan den RijnâGermantown, Md., 1980, pp. 273â310. MR 605348
- E.Viehweg. Weak positivity and the additivity of the Kodaira dimension for certain fibre spaces. Adv. Stud. in Pure Math. 1 (1983) p. 329-353.
- E.Viehweg. Canonical divisors and the additivity of the Kodaira dimension for morphisms of relative dimension one. Compositio Math. 35, Fasc 2 (1977) p. 197-223.
- E.Viehweg. Rational singularities of higher dimensional schemes. Proc. AMS. 63 n.1 (1977) p.6-8.
- Paul Vojta, Diophantine approximations and value distribution theory, Lecture Notes in Mathematics, vol. 1239, Springer-Verlag, Berlin, 1987. MR 883451, DOI 10.1007/BFb0072989
Bibliographic Information
- Lucia Caporaso
- Affiliation: Department of Mathematics, Harvard University, 1 Oxford St., Cambridge, Massachusetts 02138
- MR Author ID: 345125
- Email: caporaso@zariski.harvard.edu
- Joe Harris
- Affiliation: Department of Mathematics, Harvard University, 1 Oxford St., Cambridge, Massachusetts 02138
- Email: harris@zariski.harvard.edu
- Barry Mazur
- Affiliation: Department of Mathematics, Harvard University, 1 Oxford St., Cambridge, Massachusetts 02138
- MR Author ID: 121915
- ORCID: 0000-0002-1748-2953
- Email: mazur@zariski.harvard.edu
- Received by editor(s): September 15, 1994
- Received by editor(s) in revised form: March 23, 1995
- © Copyright 1997 American Mathematical Society
- Journal: J. Amer. Math. Soc. 10 (1997), 1-35
- MSC (1991): Primary 14G05, 14H10
- DOI: https://doi.org/10.1090/S0894-0347-97-00195-1
- MathSciNet review: 1325796