  We prove in this article that given a linearly concave domain $D$ in the
projective space $\Bbb{CP}^{n}$, a 1-dimensional comlex analytic set $V$ in
$D$, and a meromorphic 1-form $\phi$ on $V$, $V$ is a subset of an algebraic
variety of $\Bbb{CP}^{n}$ and $\phi$ is the restriction to $V$ of an algebraic
1-form on $\Bbb{CP}^{n}$ if and only if the Abel transform $A(\phi \wedge [V])$
of the analytic current $\phi \wedge [V]$ is an algebraic 1-form on
$(\Bbb{CP}^{n})*$, where an algebraic 1-form on $\Bbb{CP}^{n}$ is a meromorphic
1-form defined on a ramified analytic covering of $\Bbb{CP}^{n}$. This result
has its origin in the general inverse Abel theorems of Lie, Darboux,
Saint-Donat, Griffiths and Henkin.
