Successive minima on arithmetic varieties

C. Soulé

Compositio Mathematica (1995)

  • Volume: 96, Issue: 1, page 85-98
  • ISSN: 0010-437X

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Soulé, C.. "Successive minima on arithmetic varieties." Compositio Mathematica 96.1 (1995): 85-98. <http://eudml.org/doc/90357>.

@article{Soulé1995,
author = {Soulé, C.},
journal = {Compositio Mathematica},
keywords = {arithmetic varieties; successive minima; Faltings height; degree; surfaces of general type},
language = {eng},
number = {1},
pages = {85-98},
publisher = {Kluwer Academic Publishers},
title = {Successive minima on arithmetic varieties},
url = {http://eudml.org/doc/90357},
volume = {96},
year = {1995},
}

TY - JOUR
AU - Soulé, C.
TI - Successive minima on arithmetic varieties
JO - Compositio Mathematica
PY - 1995
PB - Kluwer Academic Publishers
VL - 96
IS - 1
SP - 85
EP - 98
LA - eng
KW - arithmetic varieties; successive minima; Faltings height; degree; surfaces of general type
UR - http://eudml.org/doc/90357
ER -

References

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  1. 1 W. Banaszczyk: New bounds in some transference theorems in the geometry of numbers, Math. Annalen, 296 (1993), 625-635. Zbl0786.11035MR1233487
  2. 2 E. Bombieri: Canonical models of surfaces of general type, Publ. Math. IHES, 42 (1973), 171-219. Zbl0259.14005MR318163
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  5. 5 J.-F. Burnol: Remarques sur la stabilité en arithmétique, International Mathematics Research Notices, Duke Math. J., 6 (1992), 117-127. Zbl0764.14006MR1167116
  6. 6 G. Faltings: Calculus on arithmetic surfaces, Annals of Math., 119 (1984), 387-424. Zbl0559.14005MR740897
  7. 7 D. Gieseker: Global moduli for surfaces of general type, Inventiones Math., 43 (1977), 233-282. Zbl0389.14006MR498596
  8. 8 D. Gieseker and I. Morrison: Hilbert stability of rank-two bundles on curves, J. Differential geometry, 19 (1984), 1-29. Zbl0573.14005MR739780
  9. 9 H. Gillet and C. Soulé: Characteristic classes for algebraic vector bundles with Hermitian metrics, I, II, Annals of Math., 131 (1990), 163-203 and 205-238. Zbl0715.14006MR1038362
  10. 10 H. Gillet and C. Soulé: On the number of lattice points in convex symmetric bodies and their duals, Israel Journal of Math., 74, no 2-3 (1991), 347-357. Zbl0752.52008MR1135244
  11. 11 D. Grayson: Reduction theory using semistability, Comment. Math. Helvetici, 59 (1984), 600-634. Zbl0564.20027MR780079
  12. 12 Y. Miyaoka: Bogomolov inequality on arithmetic surfaces, talk at the Oberwolfach conference on "Arithmetical Algebraic Geometry", G. Harder and N. Katz org. (1988). 
  13. 13 A. Moriwaki: Inequality of Bogomolov-Gieseker's type on arithmetic surfaces, Duke Math. Journal, 74 (1994), 713-761. Zbl0854.14012MR1277952
  14. 14 I. Morrison: Projective stability of ruled surfaces, Inventiones Math., 56 (1980), 269-304. Zbl0423.14005MR561975
  15. 15 D. Mumford: Stability of projective varieties, l'Ens. Math., 23 (1977), 39-110. Zbl0363.14003MR450272
  16. 16 C. Soulé: A vanishing theorem on arithmetic surfaces, Inventiones Math.116 (1994), 577-599. Zbl0834.14013MR1253205
  17. 17 U. Stuhler: Eine Bemerkung zur Reduktionstheorie Quadratischen Formen, Archiv. der Math., 27 (1976), 604-610. Zbl0338.10024MR424707
  18. 18 S. Zhang: Positive line bundles on arithmetic surfaces, Annals of Math., 136 (1992), 569-587. Zbl0788.14017MR1189866
  19. 19 S. Zhang: Positive line bundles on arithmetic varieties, preprint Princeton University (1992). MR1254133
  20. 20 S. Zhang: Geometry reductivity at archimedean places, preprint Princeton University (1993). 

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