The tautological ring of M 1,n ct
Annales de l'Institut Fourier, Volume 61 (2011) no. 7, pp. 2751-2779.

We describe the tautological ring of the moduli space of stable n-pointed curves of genus one of compact type. It is proven that it is a Gorenstein algebra.

Nous décrivons l’anneau tautologique de l’espace des modules des courbes stables de genre un de type compact avec n points marqués. On prouve que c’est une algèbre de Gorenstein.

DOI: 10.5802/aif.2793
Classification: 14H10,  14C17,  14C25,  14H52
Keywords: Moduli of curves, tautological rings
Tavakol, Mehdi 1

1 Universiteit van Amsterdam Instituut voor Wiskunde Korteweg de Vries (Netherlands
@article{AIF_2011__61_7_2751_0,
     author = {Tavakol, Mehdi},
     title = {The tautological ring of $M_{1,n}^{ct}$},
     journal = {Annales de l'Institut Fourier},
     pages = {2751--2779},
     publisher = {Association des Annales de l{\textquoteright}institut Fourier},
     volume = {61},
     number = {7},
     year = {2011},
     doi = {10.5802/aif.2793},
     mrnumber = {3112507},
     language = {en},
     url = {http://archive.numdam.org/articles/10.5802/aif.2793/}
}
TY  - JOUR
AU  - Tavakol, Mehdi
TI  - The tautological ring of $M_{1,n}^{ct}$
JO  - Annales de l'Institut Fourier
PY  - 2011
DA  - 2011///
SP  - 2751
EP  - 2779
VL  - 61
IS  - 7
PB  - Association des Annales de l’institut Fourier
UR  - http://archive.numdam.org/articles/10.5802/aif.2793/
UR  - https://www.ams.org/mathscinet-getitem?mr=3112507
UR  - https://doi.org/10.5802/aif.2793
DO  - 10.5802/aif.2793
LA  - en
ID  - AIF_2011__61_7_2751_0
ER  - 
%0 Journal Article
%A Tavakol, Mehdi
%T The tautological ring of $M_{1,n}^{ct}$
%J Annales de l'Institut Fourier
%D 2011
%P 2751-2779
%V 61
%N 7
%I Association des Annales de l’institut Fourier
%U https://doi.org/10.5802/aif.2793
%R 10.5802/aif.2793
%G en
%F AIF_2011__61_7_2751_0
Tavakol, Mehdi. The tautological ring of $M_{1,n}^{ct}$. Annales de l'Institut Fourier, Volume 61 (2011) no. 7, pp. 2751-2779. doi : 10.5802/aif.2793. http://archive.numdam.org/articles/10.5802/aif.2793/

[1] Arbarello, E.; Cornalba, M. Calculating cohomology groups of moduli spaces of curves via algebraic geometry, Inst. Hautes Études Sci. Publ. Math. (1998) no. 88, p. 97-127 (1999) | EuDML | Numdam | MR | Zbl

[2] Cornalba, M. On the projectivity of the moduli spaces of curves, J. Reine Angew. Math., Volume 443 (1993), pp. 11-20 | DOI | EuDML | MR | Zbl

[3] 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

[4] 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) (2001) no. 1232, pp. 78-87 | MR

[5] Faber, C. A remark on a conjecture of Hain and Looijenga (2008) (Arxiv preprint arXiv:0812.3631) | Zbl

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

[7] Faber, C.; Pandharipande, R. Hodge integrals, partition matrices, and the λ g conjecture, Annals of mathematics (2003), pp. 97-124 | MR | Zbl

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

[9] Fulton, W.; MacPherson, R. A compactification of configuration spaces, Ann. of Math. (2), Volume 139 (1994) no. 1, pp. 183-225 | DOI | MR | Zbl

[10] Getzler, E. Intersection theory on M ¯ 1,4 and elliptic Gromov-Witten invariants, Journal of the American Mathematical Society, Volume 10 (1997) no. 4, pp. 973 | MR | Zbl

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

[12] 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 | DOI | MR | Zbl

[13] Green, M.; Griffiths, P. An interesting 0-cycle, Duke Math. J., Volume 119 (2003) no. 2, pp. 261-313 | DOI | MR | Zbl

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

[15] Hanlon, P.; Wales, D. On the decomposition of Brauer’s centralizer algebras, J. Algebra, Volume 121 (1989) no. 2, pp. 409-445 | DOI | MR | Zbl

[16] 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 | DOI | MR | Zbl

[17] Pandharipande, R. A geometric construction of Getzler’s elliptic relation, Math. Ann., Volume 313 (1999) no. 4, pp. 715-729 | DOI | MR | Zbl

Cited by Sources: