  We prove the local well-posedness of the incompressible current-vortex sheet
problems in standard Sobolev spaces under the surface tension or the
Syrovatskij condition, which shows that both capillary forces and large
tangential magnetic fields can stabilize the motion of current-vortex sheets.
Furthermore, under the Syrovatskij condition, the vanishing surface tension
limit is established for the motion of current-vortex sheets. These results
hold without assuming the interface separating the two plasmas being a graph.
