The Second Cohomology with Symplectic Coefficients of the Moduli Space of Smooth Projective Curves
| dc.creator | Kabanov, Alexandre | |
| dc.date | 1996-11-04 | |
| dc.date.accessioned | 2026-07-07T09:07:03Z | |
| dc.date.available | 2026-07-07T09:07:03Z | |
| dc.description | Each finite dimensional irreducible rational representation V of the symplectic group Sp_{2g} determines a generically defined local system \V over the moduli space M_g of genus g smooth projective curves. We study H^2(M_g;\V) and the mixed Hodge structure on it. Specifically, we prove that if g>5, then the natural map IH^2(MS_g;\V)-->H^2(M_g;\V) is an isomorphism where MS_g is the Satake compactification of M_g. Using the work of Saito we conclude that the mixed Hodge structure on H^2(M_g;\V) is pure of weight 2+r if \V underlies a variation of Hodge structure of weight r. We also obtain estimates on the weight of the mixed Hodge structure on H^2(M_g;\V) for 2<g<6. Results of this article can be applied in the study of relations in the Torelli group T_g. | |
| dc.description | 23 pages, latex2e with amslatex and xy-pic, to appear in Compositio Mathematica | |
| dc.identifier | https://arxiv.org/abs/alg-geom/9611004 | |
| dc.identifier | http://arxiv.org/abs/alg-geom/9611004 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/150229 | |
| dc.subject | Algebraic Geometry | |
| dc.title | The Second Cohomology with Symplectic Coefficients of the Moduli Space of Smooth Projective Curves | |
| dc.type | text |