Effective bounds for semipositive sheaves and for the height of points on curves over complex function fields

Hélène Esnault; Eckart Viehweg

Compositio Mathematica (1990)

  • Volume: 76, Issue: 1-2, page 69-85
  • ISSN: 0010-437X

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Esnault, Hélène, and Viehweg, Eckart. "Effective bounds for semipositive sheaves and for the height of points on curves over complex function fields." Compositio Mathematica 76.1-2 (1990): 69-85. <http://eudml.org/doc/90055>.

@article{Esnault1990,
author = {Esnault, Hélène, Viehweg, Eckart},
journal = {Compositio Mathematica},
keywords = {geometric heights; section of surjective morphisms; Mordell conjecture over function fields},
language = {eng},
number = {1-2},
pages = {69-85},
publisher = {Kluwer Academic Publishers},
title = {Effective bounds for semipositive sheaves and for the height of points on curves over complex function fields},
url = {http://eudml.org/doc/90055},
volume = {76},
year = {1990},
}

TY - JOUR
AU - Esnault, Hélène
AU - Viehweg, Eckart
TI - Effective bounds for semipositive sheaves and for the height of points on curves over complex function fields
JO - Compositio Mathematica
PY - 1990
PB - Kluwer Academic Publishers
VL - 76
IS - 1-2
SP - 69
EP - 85
LA - eng
KW - geometric heights; section of surjective morphisms; Mordell conjecture over function fields
UR - http://eudml.org/doc/90055
ER -

References

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  1. 1 H. Esnault and E. Viehweg, Dyson's lemma for polynomials in several variables (and the theorem of Roth). Invent. Math.78 (1984) 445-490. Zbl0545.10021MR768988
  2. 2 H. Esnault and E. Viehweg, Logarithmic De Rham complexes and vanishing theorems. Invent. Math.86 (1986) 161-194. Zbl0603.32006MR853449
  3. 3 T. Fujita, On Kähler fibre spaces over curves. J. Math. Soc. Japan30 (1978) 779-794. Zbl0393.14006MR513085
  4. 4 H. Grauert, Mordell's Vermutung über rationale Punkte auf algebraischen Kurven und Funktionenkörper. Publ. Math. IHES25 (1965) 131-149. Zbl0137.40503MR222087
  5. 5 Y. Kawamata, A generalization of Kodaira-Ramanujam's vanishing theorem. Math. Ann.261 (1982) 57-71. Zbl0476.14007
  6. 6 Yu. I. Manin, Rational points on an algebraic curve over function fields. Trans. Amer. Math. Soc.50 (1966) 189-234. Zbl0178.55102
  7. 7 S. Mori, Classification of higher-dimensional varieties. Algebraic Geometry. Bowdoin1985. Proc. of Symp. in Pure Math. 46 (1987) 269-331. Zbl0656.14022MR927961
  8. 8 A.N. Parshin, Algebraic curves over function fieldsI. Math. USSR Izv.2 (1968) 1145-1170. Zbl0188.53003
  9. 9 L. Szpiro, Séminaire sur les pinceaux de courbes de genre au moins deux. Astérisque86 (1981). Zbl0463.00009MR642675
  10. 10 E. Viehweg, Vanishing theorems. J. Reine Angew. Math.335 (1982) 1-8. Zbl0485.32019MR667459
  11. 11 E. Viehweg, Weak positivity and the additivity of the Kodaira dimension for certain fibre spaces. Adv. Stud. Pure Math.1 (1983) 329-353North-Holland. Zbl0513.14019MR715656
  12. 12 E. Viehweg, Vanishing theorems and positivity in algebraic fibre spaces. Proc. Intern. Congr. Math., Berkeley1986, 682-687. Zbl0685.14013MR934270
  13. 13 E. Viehweg, Weak positivity and the stability of certain Hilbert points. Invent. Math.96 (1989) 639-667. Zbl0695.14006MR996558
  14. 14 P. Vojta, Mordell's conjecture over function fields. Preprint 1988. Zbl0662.14019
  15. 15 A.N. Parshin, Algebraic curves over function fields. Soviet Math. Dokl.9 (1968) 1419-1422. Zbl0176.50903

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