The SL(2, C) Yang-Mills instanton solutions constructed recently by the biquaternion method were shown to satisfy the complex version of the ADHM equations and the monad construction.Moreover, we discover that, in addition to the holomorphic vector bundles on CP 3 similar to the case of SU (2) ADHM construction, the SL(2, C) instanton solutions can be used to explicitly construct instanton sheaves on CP 3 . Presumably, the existence of these instanton sheaves is related to the singularities of the SL(2, C) instantons on S 4 which do not exist for SU (2) instantons. * Electronic address:

We show that there exist infinite number of recurrence relations valid for all energies among the open bosonic string scattering amplitudes (SSA) of three tachyons and one arbitrary string state, or the Lauricella SSA. Moreover, these infinite number of recurrence relations can be used to solve all the Lauricella SSA and express them in terms of one single four tachyon amplitude. These results extend the solvability of SSA at the high energy, fixed angle scattering limit and those at the Regge scattering limit discovered previously to all kinematic regimes.

We calculate a sheaf line in CP 3 which is the real line supporting sheaf points on CP 3 of SL(2, C) Yang-Mills instanton (or SU (2) complex Yang-Mills instanton) sheaves for some given ADHM data we obtained previously. We found that this sheaf line is indeed a special jumping line over S 4 spacetime. In addition, we calculate the singularity structure of the connection A and the field strength F at the corresponding singular point on S 4 of this sheaf line. We found that the order of singularity at the singular point on S 4 associated with the sheaf line in CP 3 is higher than those of other singular points associated with normal jumping lines. We conjecture that this is a general feature for sheaf lines among jumping lines. * Electronic address:

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We explicitly construct SL(2, C) (or SU (2) complex) Yang-Mills (weakly) three and four instanton sheaves on CP 3 . These results extend the previous construction of Yang-Mills (weakly) instanton sheaves with topological charge two [18]. * Electronic address: