Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Algebraic cycles on the relative symmetric powers and on the relative
  Jacobian of a family of curves. II   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.

35
The categories of this paper are: mtrl-th
24
The categories of this paper are: dg-ga
17
The categories of this paper are: q-fin
1
The categories of this paper are: cs
10
The categories of this paper are: q-bio
9
The categories of this paper are: nlin
34
The categories of this paper are: chem-ph
12
The categories of this paper are: nucl-th
33
The categories of this paper are: plasm-ph
37
The categories of this paper are: supr-con
0
The categories of this paper are: hep-ph
27
The categories of this paper are: comp-gas
6
The categories of this paper are: astro-ph
31
The categories of this paper are: ao-sci
32
The categories of this paper are: atom-ph
21
The categories of this paper are: adap-org