Relations in the tautological ring of $M_g$

Eleny-Nicoleta Ionel

Relations in the tautological ring of $M_g$

Algebraic Geometry 2007-05-23 v1

Authors: Eleny-Nicoleta Ionel

Abstract

Using a simple geometric argument, we obtain an infinite family of nontrivial relations in the tautological ring of $M_g$ (and in fact that of $M_{g,2}$ ). One immediate consequence of these relations is that the classes $\kappa_1,...,\kappa_{[g/3]}$ generate the tautological ring of $M_g$ , which has been conjectured by Faber, and recently proven at the level of {\em cohomology} by Morita.

Keywords

tautological ring moduli space of curves relations kappa classes m_g

Cite

@article{arxiv.math/0312100,
  title  = {Relations in the tautological ring of $M_g$},
  author = {Eleny-Nicoleta Ionel},
  journal= {arXiv preprint arXiv:math/0312100},
  year   = {2007}
}

Comments

24 pages

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