A remark on a conjecture of Hain and Looijenga

Carel Faber[1]

  • [1] Department of Mathematics, KTH Royal Institute of Technology, Lindstedtsvägen 25, 10044 Stockholm, Sweden.

Annales de l’institut Fourier (2011)

  • Volume: 61, Issue: 7, page 2745-2750
  • ISSN: 0373-0956

Abstract

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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.

How to cite

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Faber, Carel. "A remark on a conjecture of Hain and Looijenga." Annales de l’institut Fourier 61.7 (2011): 2745-2750. <http://eudml.org/doc/275548>.

@article{Faber2011,
abstract = {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.},
affiliation = {Department of Mathematics, KTH Royal Institute of Technology, Lindstedtsvägen 25, 10044 Stockholm, Sweden.},
author = {Faber, Carel},
journal = {Annales de l’institut Fourier},
keywords = {Moduli spaces of curves; tautological ring; Gorenstein ring; moduli spaces of curves},
language = {eng},
number = {7},
pages = {2745-2750},
publisher = {Association des Annales de l’institut Fourier},
title = {A remark on a conjecture of Hain and Looijenga},
url = {http://eudml.org/doc/275548},
volume = {61},
year = {2011},
}

TY - JOUR
AU - Faber, Carel
TI - A remark on a conjecture of Hain and Looijenga
JO - Annales de l’institut Fourier
PY - 2011
PB - Association des Annales de l’institut Fourier
VL - 61
IS - 7
SP - 2745
EP - 2750
AB - 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.
LA - eng
KW - Moduli spaces of curves; tautological ring; Gorenstein ring; moduli spaces of curves
UR - http://eudml.org/doc/275548
ER -

References

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  1. C. Faber, A conjectural description of the tautological ring of the moduli space of curves, Moduli of curves and abelian varieties (1999), 109-129, Vieweg, Braunschweig Zbl0978.14029MR1722541
  2. C. Faber, Hodge integrals, tautological classes and Gromov-Witten theory, (2001), 78-87, Sūrikaisekikenkyūsho Kōkyūroku Zbl1322.14084MR1905884
  3. C. Faber, R. Pandharipande, 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. 48 (2000), 215-252 Zbl1090.14005MR1786488
  4. C. Faber, R. Pandharipande, Relative maps and tautological classes, J. Eur. Math. Soc. (JEMS) 7 (2005), 13-49 Zbl1084.14054MR2120989
  5. T. Graber, R. Pandharipande, Constructions of nontautological classes on moduli spaces of curves, Michigan Math. J. 51 (2003), 93-109 Zbl1079.14511MR1960923
  6. T. Graber, R. Vakil, On the tautological ring of M ¯ g , n , Turkish J. Math. 25 (2001), 237-243 Zbl1040.14007MR1829089
  7. T. Graber, R. Vakil, Relative virtual localization and vanishing of tautological classes on moduli spaces of curves, Duke Math. J. 130 (2005), 1-37 Zbl1088.14007MR2176546
  8. R. Hain, E. Looijenga, Mapping class groups and moduli spaces of curves, Algebraic geometry—Santa Cruz 1995 62 (1997), 97-142, Part 2, Amer. Math. Soc., Providence, RI Zbl0914.14013MR1492535
  9. S. Keel, Intersection theory of moduli space of stable n -pointed curves of genus zero, Trans. Amer. Math. Soc. 330 (1992), 545-574 Zbl0768.14002MR1034665
  10. E. Looijenga, On the tautological ring of M g , Invent. Math. 121 (1995), 411-419 Zbl0851.14017MR1346214
  11. R. Pandharipande, Three questions in Gromov-Witten theory, (2002), 503-512, Higher Ed. Press, Beijing Zbl1047.14043MR1957060
  12. D. Petersen, The structure of the tautological ring in genus one Zbl1291.14045
  13. M. Tavakol, The tautological ring of M 1 , n c t , Ann. Inst. Fourier (Grenoble) 61.7 (2011) Zbl1323.14019
  14. M. Tavakol, The tautological ring of the moduli space M 2 , n r t , (Preprint, arXiv:1101.5242) Zbl06385573

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