Height formulas for homogeneous varieties

Michigan Mathematical Journal

Volumn 48, Issue SUPPL., 2000, Pages 593-610

  Tamvakis, Harry ^a  

^a UNIVERSITY OF PENNSYLVANIA   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0013528883     PISSN: 00262285     EISSN: None     Source Type: Journal    
DOI: 10.1307/mmj/1030132735     Document Type: Article

References (31)

1. A. Abbès and T. Bouche, Théorème de Hilbert-Samuel "arithmetique", Ann. Inst. Fourier (Grenoble) 45 (1995), 375-401.
2. I. N. Bernstein, I. M. Gelfand, and S. I. Gelfand, Schubert cells and the cohomology of the spaces G/P, Uspekhi Mat. Nauk 28 (1973), 1-26.
3. n, Adv. Math. 62 (1986), 49-67.
4. A. Borel and F. Hirzebruch, Characteristic classes and homogeneous spaces. I, Amer. J. Math. 80 (1958), 458-538.
5. J.-B. Bost, H. Gillet, and C. Soulé, Heights of protective varieties and positive Green forms. J. Amer. Math. Soc. 7 (1994), 903-1027.
6. J. Cassaigne and V. Maillot, Hauteurs des hypersitrfaces et fonctions zêta d'lgusa, preprint, 1994.
7. M. Demazure, Invariants symétriques entiers des groupes de Weyl et torsion, Invent. Math. 21 (1973), 287-301.
8. M. Demazure and A. Grothendieck, Schémas en groupes. I-III, Lecture Notes in Math., 151-153, Springer-Verlag, New York, 1970.
9. G. Faltings, Diophantine approximation on abelian varieties, Ann. of Math. (2) 133 (1991), 549-576.
10. W. Fulton, Intersection theory, Ergeb. Math. Grenzgeb. (3), 2, Springer-Verlag, Berlin, 1998.
11. H. Gillet and C. Soulé, Amplitude arithmétique, C.R. Acad. Sci. Paris Sér. I Math. 307 (1988), 887-890.
12. _, Arithmetic intersection theory, Inst. Hautes Études Sci. Publ. Math. 72 (1990), 94-174.
13. J. C. Jantzen, Representations of algebraic groups, Pure Appl. Math., 131. Academic Press, Boston, 1987.
14. C. Kaiser and K. Köhler, A fixed point formula of Lefschetz type in Arakelov geometry III: Representations of Chevalley schemes and heights of flag varieties. preprint, 1999.
15. K. Köhler and D. Roessler, A fixed point formula of Lefschetz type in Arakelov geometry I: Statement and proof, preprint, 1999.
16. I. G. Macdonald, Symmetric functions and Hall polynomials, Oxford Math. Monographs, Clarendon Press, New York, 1995.
17. V. Maillot, Un calcul de Schubert arithmétique, Duke Math. J. 80 (1995), 195-221.
18. D. G. Northcott, An inequality in the theory of arithmetic on algebraic varieties, Proc. Cambridge Philos. Soc. 45 (1949), 502-509.
19. A. L. Onishchik and E. B. Vinberg, Lie groups and algebraic groups, Springer Ser. Soviet Math., Springer-Verlag, Berlin, 1990.
20. P. Philippon, Sur des hauteurs alternatives. I, Math. Ann. 289 (1991), 255-283; II. Ann. Inst. Fourier (Grenoble) 44 (1994), 1043-1065; III, J. Math. Pures Appl. (9) 74 (1995), 345-365.
21. P. Philippon, Sur des hauteurs alternatives. I, Math. Ann. 289 (1991), 255-283; II. Ann. Inst. Fourier (Grenoble) 44 (1994), 1043-1065; III, J. Math. Pures Appl. (9) 74 (1995), 345-365.
22. P. Philippon, Sur des hauteurs alternatives. I, Math. Ann. 289 (1991), 255-283; II. Ann. Inst. Fourier (Grenoble) 44 (1994), 1043-1065; III, J. Math. Pures Appl. (9) 74 (1995), 345-365.
23. P. Pragacz, Algebro-geometric applications of Schur S-and Q-polynomials, Lecture Notes in Math., 1478, pp. 130-191, Springer-Verlag, Berlin, 1991.
24. P. Pragacz and J. Ratajski, Formulas for Lagrangian and orthogonal degeneracy loci: Q̄-polynomial approach, Compositio Math. 107 (1997), 11-87.
25. C. L. Siegel, Über einige Andwendungen diophantischer Approximationen, Abh. Preuss. Akad. Wiss. (1929), 41-69.
26. D. M. Snow, The nef value and defect of homogeneous line bundles, Trans, Amer. Math. Soc. 340 (1993), 227-241.
27. H. Tamvakis, Bott-Chern forms and arithmetic intersections, Enseign. Math. (2) 43 (1997), 33-54.
28. _, Arithmetic intersection theory on flag varieties, Math. Ann. 314 (1999), 641-665.
29. _, Schubert calculus on the arithmetic Grassmannian, Duke Math. J. 98 (1999), 421-443.
30. _, Arakelov theory of the Lagrangian Grassmannian, J. Reine Angew. Math. 516 (1999), 207-223.
31. A. Weil, Arithmetic on algebraic varieties, Ann. of Math. (2) 53 (1951), 412-444.