The Chow ring of the stack of cyclic covers of the projective line
[L’anneau d’intersection du champ des revêtements cycliques de la droite projective]
Fulghesu, Damiano ; Viviani, Filippo
Annales de l'Institut Fourier, Tome 61 (2011), p. 2249-2275 / Harvested from Numdam

Dans ce travail nous calculons l’anneau d’intersection avec des coef- ficients entiers du champ des revêtements cycliques lisses et uniformes de la droite projective. Nous explicitons aussi tous les générateurs.

In this paper we compute the integral Chow ring of the stack of smooth uniform cyclic covers of the projective line and we give explicit generators.

Publié le : 2011-01-01
DOI : https://doi.org/10.5802/aif.2672
Classification:  14D23,  14H10,  14L30,  14H45,  20G10
Mots clés: théorie de l’intersection, revêtements cycliques, champs algébriques, champs de modules des courbes
@article{AIF_2011__61_6_2249_0,
     author = {Fulghesu, Damiano and Viviani, Filippo},
     title = {The Chow ring of the stack of cyclic covers of the projective line},
     journal = {Annales de l'Institut Fourier},
     volume = {61},
     year = {2011},
     pages = {2249-2275},
     doi = {10.5802/aif.2672},
     zbl = {1254.14016},
     mrnumber = {2976310},
     language = {en},
     url = {http://dml.mathdoc.fr/item/AIF_2011__61_6_2249_0}
}
Fulghesu, Damiano; Viviani, Filippo. The Chow ring of the stack of cyclic covers of the projective line. Annales de l'Institut Fourier, Tome 61 (2011) pp. 2249-2275. doi : 10.5802/aif.2672. http://gdmltest.u-ga.fr/item/AIF_2011__61_6_2249_0/

[1] Arbarello, Enrico; Cornalba, Maurizio The Picard groups of the moduli spaces of curves, Topology, Tome 26 (1987) no. 2, pp. 153-171 | Article | MR 895568 | Zbl 0625.14014

[2] Arsie, Alessandro; Vistoli, Angelo Stacks of cyclic covers of projective spaces, Compos. Math., Tome 140 (2004) no. 3, pp. 647-666 | Article | MR 2041774 | Zbl 1169.14301

[3] Bolognesi, M.; Vistoli, A. Stacks of trigonal curves (To appear in Trans. Amer. Math. Soc. (available at arXiv:0903.0965))

[4] Deligne, P.; Mumford, D. The irreducibility of the space of curves of given genus, Inst. Hautes Études Sci. Publ. Math. (1969) no. 36, pp. 75-109 | Article | Numdam | MR 262240 | Zbl 0181.48803

[5] Edidin, Dan; Fulghesu, D. The integral Chow ring of the stack of hyperelliptic curves of even genus, Math. Research Letter (2008) no. 15, pp. 10001-10015 | MR 2480558 | Zbl 1174.14006

[6] Edidin, Dan; Graham, William Equivariant intersection theory, Invent. Math., Tome 131 (1998) no. 3, pp. 595-634 | Article | MR 1614555 | Zbl 0940.14003

[7] Faber, Carel Chow rings of moduli spaces of curves, Ann. of Math. (2), Tome 132 (1990) no. 2, pp. 331-419 | Article | MR 1070600 | Zbl 0721.14013

[8] Gorchinskiy, Sergey; Viviani, Filippo Picard group of moduli of hyperelliptic curves, Math. Z., Tome 258 (2008) no. 2, pp. 319-331 | Article | MR 2357639 | Zbl 1132.14011

[9] Izadi, E. The Chow ring of the moduli space of curves of genus 5, The moduli space of curves (Texel Island, 1994), Birkhäuser Boston, Boston, MA (Progr. Math.) Tome 129 (1995), pp. 267-304 | MR 1363060 | Zbl 0862.14016

[10] Mumford, David Geometric invariant theory, Springer-Verlag, Berlin, Ergebnisse der Mathematik und ihrer Grenzgebiete, Neue Folge, Band 34 (1965) | MR 214602 | Zbl 0147.39304

[11] Mumford, David Towards an enumerative geometry of the moduli space of curves, Arithmetic and geometry, Vol. II, Birkhäuser Boston, Boston, MA (Progr. Math.) Tome 36 (1983), pp. 271-328 | MR 717614 | Zbl 0554.14008

[12] Pandharipande, Rahul Equivariant Chow rings of O(k), SO (2k+1), and SO (4), J. Reine Angew. Math., Tome 496 (1998), pp. 131-148 | Article | MR 1605814 | Zbl 0905.14026

[13] Totaro, Burt The Chow ring of a classifying space, Algebraic K-theory (Seattle, WA, 1997), Amer. Math. Soc., Providence, RI (Proc. Sympos. Pure Math.) Tome 67 (1999), pp. 249-281 | MR 1743244 | Zbl 0967.14005

[14] Vezzosi, Gabriele On the Chow ring of the classifying stack of PGL 3,C , J. Reine Angew. Math., Tome 523 (2000), pp. 1-54 | Article | MR 1762954 | Zbl 0967.14006

[15] Vistoli, Angelo The Chow ring of 2 , Invent. Math., Tome 131 (1998) no. 3, pp. 635-644 | Article | MR 1614559