Intersection-theoretical computations on ${\οverline M}_{g}$

• Autorzy: Carel Faber
• Języki publikacji: EN

Abstrakty

EN

In this paper we explore several concrete problems, all more or less related to the intersection theory of the moduli space of (stable) curves, introduced by Mumford [Mu 1].

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Banach Center Publications
• Rocznik: 1996
• Tom: 36
• Numer: 1
• Strony: 71-81

Daty

wydano

1996

Twórcy

autor

Carel Faber

• Faculteit der Wiskunde en Informatica, Universiteit van Amsterdam, Plantage Muidergracht 24, 1018 TV Amsterdam, Netherlands

Bibliografia

• [A-C] E. Arbarello and M. Cornalba, The Picard groups of the moduli spaces of curves, Topology 26 (1987), 153-171.
• [BCOV] M. Bershadsky, S. Cecotti, H. Ooguri and C. Vafa, Kodaira-Spencer Theory of Gravity and Exact Results for Quantum String Amplitudes, Comm. Math. Phys. 165 (1994), 311-428.
• [C-H] M. Cornalba and J. Harris, Divisor classes associated to families of stable varieties, with applications to the moduli space of curves, Ann. Scient. École Norm. Sup. (4) 21 (1988), 455-475.
• [Fa 1] C. Faber, Chow rings of moduli spaces of curves I: The Chow ring of $οverline M_3$, Ann. of Math. 132 (1990), 331-419.
• [Fa 2] C. Faber, Chow rings of moduli spaces of curves II: Some results on the Chow ring of $οverline M_4$, Ann. of Math. 132 (1990), 421-449.
• [Fa 3] C. Faber, Some results on the codimension-two Chow group of the moduli space of curves, in: Algebraic Curves and Projective Geometry (eds. E. Ballico and C. Ciliberto), Lecture Notes in Math. 1389, Springer, Berlin, 1988, 66-75.
• [Ha] R. Hartshorne, Ample Subvarieties of Algebraic Varieties, Lecture Notes in Math. 156, Springer, Berlin, 1970.
• [Hi 1] F. Hirzebruch, Automorphe Formen und der Satz von Riemann-Roch, in: Symposium Internacional de Topologí a Algebraica (México 1956), Universidad Nacional Autónoma de México and UNESCO, Mexico City, 1958, 129-144; or: Gesammelte Abhandlungen, Band I, Springer, Berlin, 1987, 345-360.
• [Hi 2] F. Hirzebruch, Characteristic numbers of homogeneous domains, in: Seminars on analytic functions, vol. II, IAS, Princeton 1957, 92-104; or: Gesammelte Abhandlungen, Band I, Springer, Berlin, 1987, 361-366.
• [Ko] M. Kontsevich, Intersection Theory on the Moduli Space of Curves and the Matrix Airy Function, Comm. Math. Phys. 147 (1992), 1-23.
• [Liu] Qing Liu, Courbes stables de genre 2 et leur schéma de modules, Math. Ann. 295 (1993), 201-222.
• [Mu 1] D. Mumford, Towards an enumerative geometry of the moduli space of curves, in: Arithmetic and Geometry II (eds. M. Artin and J. Tate), Progr. Math. 36 (1983), Birkhäuser, 271-328.
• [Mu 2] D. Mumford, On the Kodaira Dimension of the Siegel Modular Variety, in: Algebraic Geometry-Open Problems (eds. C. Ciliberto, F. Ghione and F. Orecchia), Lecture Notes in Math. 997, Springer, Berlin, 1983, 348-375.
• [Wi] E. Witten, Two dimensional gravity and intersection theory on moduli space, in: Surveys in Differential Geometry (Cambridge, MA, 1990), Lehigh Univ., Bethlehem, PA, 1991, 243-310.