Algebraic cycles on the relative symmetric powers and on the relative Jacobian of a family of curves. II
| dc.creator | Moonen, Ben | |
| dc.creator | Polishchuk, Alexander | |
| dc.date | 2008-05-23 | |
| dc.date | 2009-04-25 | |
| dc.date.accessioned | 2026-07-07T13:08:07Z | |
| dc.date.available | 2026-07-07T13:08:07Z | |
| dc.description | Let C be a curve over a non-singular base variety S. We study algebraic cycles on the symmetric powers C^[n] and on the Jacobian J. The Chow homology of C^[*], the sum of all C^[n], is a ring using the Pontryagin product. We prove that this ring is isomorphic to CH(J)[t]<u>, the PD-polynomial algebra (variable: u) over the usual polynomial ring (variable: t) over the Chow ring CH(J). We give two such isomorphisms that over a general base are different. Further we give some precise results on how CH(J) sits embedded in CH(C^[*]) and we give an explicit geometric description of how the derivations with regard to t and u act. Our results give rise to a new grading on the Chow ring of the Jacobian. After tensoring with Q the associated descending filtration coincides with the one coming from Beauville's decomposition. The grading we obtain is in general different from Beauville's. Finally we give a version of our main result for tautological classes, and we show how our methods give a very simple and geometric proof of some relations obtained by Herbaut and van der Geer-Kouvidakis. | |
| dc.description | 43 pages; the former section 1 has been moved to a new paper, arXiv:0904.3995; minor corrections and improvements | |
| dc.identifier | https://arxiv.org/abs/0805.3621 | |
| dc.identifier | http://arxiv.org/abs/0805.3621 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/228320 | |
| dc.subject | Algebraic Geometry | |
| dc.subject | 14C15, 14C25, 14H40 | |
| dc.title | Algebraic cycles on the relative symmetric powers and on the relative Jacobian of a family of curves. II | |
| dc.type | text |