Calculating cohomology groups of moduli spaces of curves via algebraic geometry
Publications Mathématiques de l'IHÉS, Tome 88 (1998), pp. 97-127.
@article{PMIHES_1998__88__97_0,
     author = {Arbarello, Enrico and Cornalba, Maurizio},
     title = {Calculating cohomology groups of moduli spaces of curves via algebraic geometry},
     journal = {Publications Math\'ematiques de l'IH\'ES},
     pages = {97--127},
     publisher = {Institut des Hautes \'Etudes Scientifiques},
     volume = {88},
     year = {1998},
     mrnumber = {2001h:14030},
     zbl = {0991.14012},
     language = {en},
     url = {http://archive.numdam.org/item/PMIHES_1998__88__97_0/}
}
TY  - JOUR
AU  - Arbarello, Enrico
AU  - Cornalba, Maurizio
TI  - Calculating cohomology groups of moduli spaces of curves via algebraic geometry
JO  - Publications Mathématiques de l'IHÉS
PY  - 1998
SP  - 97
EP  - 127
VL  - 88
PB  - Institut des Hautes Études Scientifiques
UR  - http://archive.numdam.org/item/PMIHES_1998__88__97_0/
LA  - en
ID  - PMIHES_1998__88__97_0
ER  - 
%0 Journal Article
%A Arbarello, Enrico
%A Cornalba, Maurizio
%T Calculating cohomology groups of moduli spaces of curves via algebraic geometry
%J Publications Mathématiques de l'IHÉS
%D 1998
%P 97-127
%V 88
%I Institut des Hautes Études Scientifiques
%U http://archive.numdam.org/item/PMIHES_1998__88__97_0/
%G en
%F PMIHES_1998__88__97_0
Arbarello, Enrico; Cornalba, Maurizio. Calculating cohomology groups of moduli spaces of curves via algebraic geometry. Publications Mathématiques de l'IHÉS, Tome 88 (1998), pp. 97-127. http://archive.numdam.org/item/PMIHES_1998__88__97_0/

[1] E. Arbarello, M. Cornalba Combinatorial and algebro-geometric cohomology classes on the moduli spaces of curves, J. Alg. Geom. 5 (1996), 705-749. | MR | Zbl

[2] M. Boggi, M. Pikaart, Galois covers of moduli of curves, preprint 1997. | Zbl

[3] M. Cornalba, On the projectivity of the moduli spaces of curve, J. reine angew. Math. 443 (1993), 11-20. | MR | Zbl

[4] P. Deligne, Théorie de Hodge III, I.H.E.S. Publ. Math. 44 (1974), 5-77. | Numdam | MR | Zbl

[5] C. Faber, Chow rings of moduli spaces of curves, thesis, Universiteit van Amsterdam, 1988.

[6] E. Getzler, The semi-classical approximation for modular operads, Comm. Math. Phys. 194 (1998) 481-492. | MR | Zbl

[7] E. Getzler, Topological recursion relations in genus 2, math.AG/9801003. | Zbl

[8] J. Harer, The second homology group of the mapping class group of an orientable surface, Inv. Math. 72 (1982), 221-239. | MR | Zbl

[9] J. Harer, The virtual cohomological dimension of the mapping class group of an orientable surface, Inv. Math. 84 (1986), 157-176. | MR | Zbl

[10] J. Harer, The third homology group of the moduli space of curves, Duke Math. J. 65 (1991), 25-55. | MR | Zbl

[11] J. Harer, The fourth homology group of the moduli space of curves, to appear.

[12] J. Harris, David Mumford, On the Kodaira dimension of the moduli space of curves, Inv. Math. 67 (1982), 23-86. | MR | Zbl

[13] S. Keel, Intersection theory of moduli space of stable N-pointed curves of genus zero, Trans. AMS 330 (1992), 545-574. | MR | Zbl

[14] E. Looijenga, Cohomology of ℳ3 and ℳ¹3, in “Mapping class groups and moduli spaces of Riemann surfaces” (C.F. Bödigheimer and R. M. Hain, eds.), Contemp. Math. 150, Amer. Math. Soc., Providence, RI, 1993, pp. 205-228. | MR | Zbl

[15] E. Looijenga, Smooth Deligne-Mumford compactifications by means of Prym level structures, J. Alg. Geom. 3 (1994), 283-293. | MR | Zbl

[16] E. Looijenga, Cellular decompositions of compactified moduli spaces of pointed curves, in “The Moduli Space of Curves” (R. Dijkgraaf, C. Faber, G. van der Geer, eds.), Progress in Mathematics 12, Birkhauser, Boston, (1995), 369-399. | MR | Zbl

[17] D. Mumford, Stability of projective varieties, L'Ens. Math. 23 (1977), 39-110. | MR | Zbl

[18] D. Mumford, Towards an enumerative geometry of the moduli space of curves, in “Arithmetic and Geometry”, (M. Artin, J. Tate, eds), 2, Birkhäuser, Boston (1983), 271-328. | MR | Zbl