Chow group of 1-cycles on the moduli space of vector bundles of rank 2 over a curve

Let X be a non-singular complex projective curve of genus ≥3. Choose a point x ∈ X. Let M_x be the moduli space of stable bundles of rank 2 with determinant We prove that the Chow group CH^Q₁(M_x) of 1-cycles on M_x with rational coefficients is isomorphic to CH^Q₀(X). By studying the rational curves on M_x, it is not difficult to see that there exits a natural homomorphism CH₀(J)→CH₁(M_x) where J denotes the Jacobian of X. The crucial point is to show that this homomorphism induces a homomorphism CH₀(X)→CH₁(M_x), namely, to go from the infinite dimensional object CH₀(J) to the finite dimensional object CH₀(X). This is proved by relating the degeneration of Hecke curves on M_x to the second term I^*2 of Bloch's filtration on CH₀(J). Insong Choe was supported by KOSEF (R01-2003-000-11634-0).