Relations in the tautological ring of $\mathcal{M}_g$
Ionel, Eleny-Nicoleta
Duke Math. J., Tome 126 (2005) no. 1, p. 157-186 / Harvested from Project Euclid
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Using a simple geometric argument, we obtain an infinite family of nontrivial relations in the tautological ring of $\mathcal{M}_g$ (coming, in fact, from relations in the Chow ring of $\overline{\mathcal{M}}_{g,2}$ ). One immediate consequence of these relations is that the classes $\kappa_1,\ldots,\kappa_{[g/3]}$ generate the tautological ring of $\mathcal{M}_g$ , which was conjectured by Faber in [F] and recently proven at the level of cohomology by Morita in [M].
Publié le : 2005-07-15
Classification:  14H10 
@article{1121448867,
     author = {Ionel, Eleny-Nicoleta},
     title = {Relations in the tautological ring of $\mathcal{M}\_g$},
     journal = {Duke Math. J.},
     volume = {126},
     number = {1},
     year = {2005},
     pages = { 157-186},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1121448867}
}

Ionel, Eleny-Nicoleta. Relations in the tautological ring of $\mathcal{M}_g$. Duke Math. J., Tome 126 (2005) no. 1, pp.  157-186. http://gdmltest.u-ga.fr/item/1121448867/