Relative Bogomolov's inequality and the cone of positive divisors on the moduli space of stable curves

Journal of the American Mathematical Society

Volumn 11, Issue 3, 1998, Pages 569-600

  Moriwaki, Atsushi ^a  

^a KYOTO UNIVERSITY   (Japan)

Author keywords

Bogomolov's inequality; Moduli space; Stable curve

Indexed keywords

EID: 0032361473     PISSN: 08940347     EISSN: None     Source Type: Journal    
DOI: 10.1090/s0894-0347-98-00261-6     Document Type: Article

References (21)

1. F. A. Bogomolov, Holomorphic tensors and vector bundles on projective varieties. Math. USSR-Izv., 13 (1978), 499-555. MR 8Oj:14014
2. J.-B. Bost, Semi-stability and height of cycles, Invent. Math., 118 (1994), 223-253. MR 95j:14024
3. M. Cornalba and J, Harris. Divisor classes associated to families of stable varieties, with application to the moduli space of curves. Ann. Scient. Ec. Norm. Sup., 21 (1988), 455-475. MR 89j:14019
4. P. Deligne and D. Mumford, The irreducibility of the space of curves of given genus, Publ. Math. IHES, 36 (1969), 75-110. MR 41:6850
5. W. Pulton, Intersection Theory, Ergebnisse der Mathematik und ihrer Grenzgebiete, 3. Folge, Band 2, (1984), Springer-Verlag. MR 85k:14004
6. D. Gieseker, Stable vector bundles and the Frobenius morphism, Ann. Scient. Ec. Norm. Sup., 6(1973) 95-101. MR 48:3963
7. D. Gieseker, On a theorem of Bogomolov on Chern classes of stable bundles, Amer. J. Math., 101 (1979), 79-85. MR 80j:14015
8. R. Hartshorne, Ample vector bundles on curves, Nagoya Math. J. 43 (1971) 73-90. MR 45:1929
9. J.-P. Jouanolou, Théorèmes de Bertini et Applications, Birkhäuser (1983). MR 86b:13007
10. F. Knudsen and D. Mumford, The projectivity of the moduli space of stable curves, I: Preliminaries on "det" and "Div", Math. Scand. 39 (1976), 19-55. MR 55:10465
11. M. Maruyama, The theorem of Grauer-Mulich-Spindler, Math. Ann. 255 (1981), 317-333. MR 82k:14012
12. Y. Miyaoka, The Chern Classes and Kodaira Dimension of a Minimal Variety, Advanced Studies in Pure Mathematics 10, 1987, Algebraic Geometry, Sendai, 1985, 449-476, Kinokuniya. MR 89k:14022
13. A. Moriwaki, Arithmetic Bogomolov-Gieseker's inequality, Amer. J. Math. 117 (1995), 1325-1347. MR 96i:14022
14. A. Moriwaki, Bogomolov conjecture over function fields for stable curves with only irreducible fibers, Comp. Math. 105 (1997), 125-140. CMP 97:10
15. A. Moriwaki, Bogomolov conjecture for curves of genus 2 over function fields, J. Math. Kyoto Univ. 36 (1996), 687-695. CMP 97:11
16. A. Moriwaki, A sharp slope inequality for general stable fibrations of curves, J. reine angew. Math. 480 (1996), 177-195. MR 97m:14029
17. D. Mumford, Stability of projective varieties, L'Enseignement Math., 23 (1977), 39-110. MR 56:8568
18. A. Paranjape and S. Ramanan, On the canonical ring of an algebraic curve, Algebraic Geometry and Commutative Algebra in Honor of Masayoshi NAGATA, vol. II (1987), 501-516 MR 90b:14024
19. E. Ullnio, Positivité et discretion des points algébriques des courbes, preprint.
20. G. Xiao, Fibered algebraic surfaces with low slope, Math. Ann., 276 (1987), 449-466. MR 88a:14046
21. S. Zhang, Admissible pairing on a curve, Invent. Math., 112 (1993), 171-193. MR 94h:14023