On Abel-Jacobi maps of moduli of parabolic bundles over a curve

Motives of moduli spaces of bundles on curves via variation of stability and flips

“…In particular, the motive 𝔥( 𝛼 ) depends on 𝛼, as was already known for the Poincaré polynomial [8,38]. As a corollary of these motivic formulae, we obtain descriptions of the Chow groups of 1-cycles (see Corollaries 5.18 and 5.21) strengthening and slightly correcting [20,21] and for fixed 𝑖, a stabilization result for CH 𝑖 ( 𝛼 ) (see Corollary 5.22).…”

“…By [18,Proposition 5.3], if 𝛼 ∈  𝑚 is a generic weight that is sufficiently small (i.e in a chamber whose closure contains the origin 0), then 𝛼 and 0 are not separated by any wall and consequently we obtain the following special case of the above result. As an application, we compute the intermediate Jacobian of 1-cycles for the moduli spaces  𝛼  of parabolic vector bundles with fixed determinant †  for a generic weight 𝛼; this strengthens the results of Chakraborty [20, Theorem 1.2] and [21,Proposition 3.4] to integral coefficients.…”

“…As an application, we compute the intermediate Jacobian of 1‐cycles for the moduli spaces $$\mathcal {N}^\alpha _\mathcal {L}$$ of parabolic vector bundles with fixed determinant $$\mathcal {L}$$ for a generic weight $$\alpha$$; this strengthens the results of Chakraborty [20, Theorem 1.2] and [21, Proposition 3.4] to integral coefficients. Corollary Fix invariants $$\eta = (n,d,m)$$ with $$m$$ corresponding to full flags.…”