Heights and reductions of semi-stable varieties

Shouwu Zhang

Compositio Mathematica (1996)

  • Volume: 104, Issue: 1, page 77-105
  • ISSN: 0010-437X

How to cite

top

Zhang, Shouwu. "Heights and reductions of semi-stable varieties." Compositio Mathematica 104.1 (1996): 77-105. <http://eudml.org/doc/90481>.

@article{Zhang1996,
author = {Zhang, Shouwu},
journal = {Compositio Mathematica},
keywords = {projective heights; Chow variety; semistability},
language = {eng},
number = {1},
pages = {77-105},
publisher = {Kluwer Academic Publishers},
title = {Heights and reductions of semi-stable varieties},
url = {http://eudml.org/doc/90481},
volume = {104},
year = {1996},
}

TY - JOUR
AU - Zhang, Shouwu
TI - Heights and reductions of semi-stable varieties
JO - Compositio Mathematica
PY - 1996
PB - Kluwer Academic Publishers
VL - 104
IS - 1
SP - 77
EP - 105
LA - eng
KW - projective heights; Chow variety; semistability
UR - http://eudml.org/doc/90481
ER -

References

top
  1. [Bo] Bost, J-B.: Semi-stability and heights of cycles, Preprint, I.H.E.S., 1993. MR1292112
  2. [B-G-S] Bost, J., Gillet, H. and Soulé, C.: Heights of projective varieties and positive Green forms, I. H. E. S., Preprint, 1993. Zbl0973.14013
  3. [Bu] Burnol, J-F.: Remarques sur les la stabilité en arimétique, International Mathematics Research Notices, Duke Math. J.6 (1992) 117-127. Zbl0764.14006MR1167116
  4. [C-H] Cornalba, M. and Harris, J.: Divisors classes associated to families of stable varieties, with applications to the moduli spaces of stable curves, Ann. Scient. Ec. Norm. Sup.21 (1988) 455—475. Zbl0674.14006
  5. [D] Deligne, P.: Le déterminant de la cohomologie, Contemporary Math.67 (1987) 93-177. Zbl0629.14008MR902592
  6. [D-M] Deligne, P. and Mumford, D.: The irreducibility of the space of curves of given genus, I.H.E.S.36 (1969) 75-109. Zbl0181.48803MR262240
  7. [D-T] Ding, W. and Tian, G.: Kdhler-Eistein matrics and the generalized Futaki invariant, Invent. Math.110 (1992). Zbl0779.53044MR1185586
  8. [E1] Elkik, R.: Fibrés d'intersection et intégrales de classes de Chern, Ann. Sci. Ecole. Norm. Sup.22 (1989) 195-226. Zbl0701.14003MR1005159
  9. [E2] Elkik, R.: Métriques sur les fibrés d'intersection, Duke Math. J.61 (1990) 303-328. Zbl0706.14008MR1068389
  10. [Fa] Faltings, G.: Diophantine approximation on abelian varieties, Ann. of Math.119' (1991) 549-576. Zbl0734.14007MR1109353
  11. [F-M] Fogarty, J. and Mumford, D.: Geometric invariant theory (2nd ed.) Springer-Verlag, Berlin, 1982. Zbl0504.14008MR719371
  12. [Fr1] Franke, J.: Chow categories, Algebraic Geometry, Berlin1988, Compositio Math.76 (1990) 101-162. Zbl0726.14005MR1078860
  13. [Fr2] Franke, J.: Chern functors, Arithmetic algebraic geometry, Texel, Progress in Math.89, Birkhäuser, (1989) 75-152. Zbl0742.14007MR1085257
  14. [G] Gieseker, D.: Global moduli for surfaces of general type, Invent. Math.43 (1977) 233-282. Zbl0389.14006MR498596
  15. [H] Hömander, L.: The analysis of linear partial differential operators I, Springer-Verlag, 1983. Zbl0521.35001MR717035
  16. [K-N] Kempf, G. and Ness, L.: The length of vectors in representation spaces, Lect. N. in Math.732 (1979) 233-243. Zbl0407.22012MR555701
  17. [M] Mumford, D.: Stability of projective varieties, L'Ens. Math.23 (1977) 39-110. Zbl0363.14003MR450272
  18. [P] Philippon, P.: Sur des hauteur alternatives I, Math. Ann.289 (1991) 255-283. Zbl0726.14017MR1092175
  19. [Se] Seshadri, C.S.: Geometric reductivity over an arbitrary base, Adv. Math.26 (1977) 225-274. Zbl0371.14009MR466154
  20. [So1] Soulé, C.: Géometrie d'Arakelov et théorie des nombres trancendants, in Journées arithmetiques de Luminy, 1989, Astérique, 198-200 (1991) 355-371. Zbl0756.14014MR1144338
  21. [So2] Soulé, C.: Successive minima on arithmetic varieties, Preprint, 1993. 
  22. [T] Tian, G.: Kähler-Eistein metrics on algebraic manifolds, ICM (1990). Zbl0747.53038MR1159246
  23. [V] Viehweg, E.: Weak positivity and the stability of certain Hilbert points I, II, III, Invent. Math.96 (1989), 639-667; 101 (1990) 191-223; 101 (1990) 521-543. Zbl0746.14014MR996558
  24. [Y1] Yau, S.T.: On the Ricci curvature of a compact Kähler manifold and complex Monge-Ampère equation, I, Comm. on Pure and Appl. Math.XXXI (1978) 339-411. Zbl0369.53059MR480350
  25. [Y2] Yau, S.T.: Nonlinear analysis in geometry, Monographic no33 de l'Enseignement Mathématique, Genéve, 1986. Zbl0631.53003MR865650
  26. [Z1] Zhang, S.: Positive line bundles on arithmetic varieties, J.A.M.S.8 (1) (1995) 187-221. Zbl0861.14018MR1254133
  27. [Z2] Zhang, S.: Geometric reductivity at archimedean places, I.M.R.N.10 (1994) 425-433. Zbl0860.14007MR1307474

NotesEmbed ?

top

You must be logged in to post comments.