We describe the tautological ring of the moduli space of stable -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 points marqués. On prouve que c’est une algèbre de Gorenstein.
Keywords: Moduli of curves, tautological rings
Mot clés : anneau tautologique, espace de modules des courbes
@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://www.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 SP - 2751 EP - 2779 VL - 61 IS - 7 PB - Association des Annales de l’institut Fourier UR - http://www.numdam.org/articles/10.5802/aif.2793/ DO - 10.5802/aif.2793 LA - en ID - AIF_2011__61_7_2751_0 ER -
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://www.numdam.org/articles/10.5802/aif.2793/
[1] 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] On the projectivity of the moduli spaces of curves, J. Reine Angew. Math., Volume 443 (1993), pp. 11-20 | DOI | EuDML | MR | Zbl
[3] 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] 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] A remark on a conjecture of Hain and Looijenga (2008) (Arxiv preprint arXiv:0812.3631) | Numdam | Zbl
[6] 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] Hodge integrals, partition matrices, and the conjecture, Annals of mathematics (2003), pp. 97-124 | MR | Zbl
[8] Relative maps and tautological classes, J. Eur. Math. Soc. (JEMS), Volume 7 (2005) no. 1, pp. 13-49 | DOI | EuDML | MR | Zbl
[9] A compactification of configuration spaces, Ann. of Math. (2), Volume 139 (1994) no. 1, pp. 183-225 | DOI | MR | Zbl
[10] Intersection theory on and elliptic Gromov-Witten invariants, Journal of the American Mathematical Society, Volume 10 (1997) no. 4, pp. 973 | MR | Zbl
[11] Constructions of nontautological classes on moduli spaces of curves, Michigan Math. J., Volume 51 (2003) no. 1, pp. 93-109 | DOI | MR | Zbl
[12] 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] An interesting 0-cycle, Duke Math. J., Volume 119 (2003) no. 2, pp. 261-313 | DOI | MR | Zbl
[14] 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] On the decomposition of Brauer’s centralizer algebras, J. Algebra, Volume 121 (1989) no. 2, pp. 409-445 | DOI | MR | Zbl
[16] Intersection theory of moduli space of stable -pointed curves of genus zero, Trans. Amer. Math. Soc., Volume 330 (1992) no. 2, pp. 545-574 | DOI | MR | Zbl
[17] A geometric construction of Getzler’s elliptic relation, Math. Ann., Volume 313 (1999) no. 4, pp. 715-729 | DOI | MR | Zbl
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