Extensions and rank-2 vector bundles on irreducible nodal curves

We generalize Bertram's work on rank two vector bundles to an irreducible projective nodal curve C. We use the natural rational map Phi(L) : P(Ext(C)(1) (L, O-C)) -> SUC (2, L) subset of C SUC (2, L) defined by Phi(L) ([0 -> O-C -> E -> L -> 0]) = E to study a compactification SUC (2, L) of the moduli space SUC (2, L) of semi-stable vector bundles of rank 2 and determinant L on C. In particular, we resolve the indeterminancy of Phi(L) in the case deg L = 3, 4 via a sequence of three blow-ups with smooth centers.