no. 7
A remark on a conjecture of Hain and Looijenga
[Une remarque sur une conjecture de Hain et Looijenga]
Faber, Carel1
1 Department of Mathematics, KTH Royal Institute of Technology, Lindstedtsvägen 25, 10044 Stockholm, Sweden.
Annales de l'Institut Fourier, Tome 61 (2011) no. 7, pp. 2745-2750.

Nous montrons que la généralisation naturelle d’une conjecture de Hain et Looijenga au cas des courbes épointées tient pour tout g et n si et seulement si les anneaux tautologiques des espaces des modules des courbes à queues rationnelles et des courbes stables sont des anneaux de Gorenstein.

We show that the natural generalization of a conjecture of Hain and Looijenga to the case of pointed curves holds for all g and n if and only if the tautological rings of the moduli spaces of curves with rational tails and of stable curves are Gorenstein.

DOI : 10.5802/aif.2792
Classification : 14H10, 13H10
Keywords: Moduli spaces of curves, tautological ring, Gorenstein ring
Mot clés : Espaces de module des courbes, anneau tautologique, anneau de Gorenstein

Faber, Carel 1

1 Department of Mathematics, KTH Royal Institute of Technology, Lindstedtsvägen 25, 10044 Stockholm, Sweden. 
@article{AIF_2011__61_7_2745_0,
     author = {Faber, Carel},
     title = {A remark on a conjecture of {Hain} and {Looijenga}},
     journal = {Annales de l'Institut Fourier},
     pages = {2745--2750},
     publisher = {Association des Annales de l{\textquoteright}institut Fourier},
     volume = {61},
     number = {7},
     year = {2011},
     doi = {10.5802/aif.2792},
     mrnumber = {3112506},
     zbl = {1278.14037},
     language = {en},
     url = {https://aif.centre-mersenne.org/articles/10.5802/aif.2792/}
}
TY  - JOUR
AU  - Faber, Carel
TI  - A remark on a conjecture of Hain and Looijenga
JO  - Annales de l'Institut Fourier
PY  - 2011
SP  - 2745
EP  - 2750
VL  - 61
IS  - 7
PB  - Association des Annales de l’institut Fourier
UR  - https://aif.centre-mersenne.org/articles/10.5802/aif.2792/
DO  - 10.5802/aif.2792
LA  - en
ID  - AIF_2011__61_7_2745_0
ER  - 
%0 Journal Article
%A Faber, Carel
%T A remark on a conjecture of Hain and Looijenga
%J Annales de l'Institut Fourier
%D 2011
%P 2745-2750
%V 61
%N 7
%I Association des Annales de l’institut Fourier
%U https://aif.centre-mersenne.org/articles/10.5802/aif.2792/
%R 10.5802/aif.2792
%G en
%F AIF_2011__61_7_2745_0
Faber, Carel. A remark on a conjecture of Hain and Looijenga. Annales de l'Institut Fourier, Tome 61 (2011) no. 7, pp. 2745-2750. doi : 10.5802/aif.2792. https://aif.centre-mersenne.org/articles/10.5802/aif.2792/

[1] Faber, C. A conjectural description of the tautological ring of the moduli space of curves, Moduli of curves and abelian varieties (Aspects Math., E33), Vieweg, Braunschweig, 1999, pp. 109-129 | MR | Zbl

[2] Faber, C. Hodge integrals, tautological classes and Gromov-Witten theory (Proceedings of the Workshop “Algebraic Geometry and Integrable Systems related to String Theory” (Kyoto, 2000)), Sūrikaisekikenkyūsho Kōkyūroku, 2001 no. 1232, pp. 78-87 | MR

[3] Faber, C.; Pandharipande, R. Logarithmic series and Hodge integrals in the tautological ring, with an appendix by Don Zagier. Dedicated to William Fulton on the occasion of his 60th birthday. Michigan Math. J., Volume 48 (2000), pp. 215-252 | MR | Zbl

[4] Faber, C.; Pandharipande, R. Relative maps and tautological classes, J. Eur. Math. Soc. (JEMS), Volume 7 (2005) no. 1, pp. 13-49 | MR | Zbl

[5] Graber, T.; Pandharipande, R. Constructions of nontautological classes on moduli spaces of curves, Michigan Math. J., Volume 51 (2003) no. 1, pp. 93-109 | MR | Zbl

[6] Graber, T.; Vakil, R. On the tautological ring of M ¯ g,n , Turkish J. Math., Volume 25 (2001) no. 1, pp. 237-243 | MR | Zbl

[7] Graber, T.; Vakil, R. Relative virtual localization and vanishing of tautological classes on moduli spaces of curves, Duke Math. J., Volume 130 (2005) no. 1, pp. 1-37 | MR | Zbl

[8] Hain, R.; Looijenga, E. Mapping class groups and moduli spaces of curves, Algebraic geometry—Santa Cruz 1995 (Proc. Sympos. Pure Math.), Volume 62, Part 2, Amer. Math. Soc., Providence, RI, 1997, pp. 97-142 | MR | Zbl

[9] Keel, S. Intersection theory of moduli space of stable n-pointed curves of genus zero, Trans. Amer. Math. Soc., Volume 330 (1992) no. 2, pp. 545-574 | MR | Zbl

[10] Looijenga, E. On the tautological ring of M g , Invent. Math., Volume 121 (1995) no. 2, pp. 411-419 | MR | Zbl

[11] Pandharipande, R. Three questions in Gromov-Witten theory (Proceedings of the International Congress of Mathematicians, Vol. II (Beijing, 2002)), Higher Ed. Press, Beijing, 2002, pp. 503-512 | MR | Zbl

[12] Petersen, D. The structure of the tautological ring in genus one (Preprint, arXiv:1205.1586)

[13] Tavakol, M. The tautological ring of M 1,n ct , Ann. Inst. Fourier (Grenoble), Volume 61.7 (2011)

[14] Tavakol, M. The tautological ring of the moduli space M 2,n rt , Preprint, arXiv:1101.5242

Cité par Sources :