We study global vortices coupled to (2+1)-dimensional gravity with a n
egative cosmological constant. We found nonsingular vortex solutions i
n phi(4) theory with a broken U(1) symmetry, of which the spacetimes d
o not involve a physical curvature singularity. When the magnitude of
a negative cosmological constant is larger than a critical value at a
given symmetry breaking scale, the spacetime structure is a regular hy
perbola; however, it becomes a charged black hole when the magnitude o
f the cosmological constant is less than the critical value. We explai
n through a duality transformation the reason why a static global vort
ex which is electrically neutral forms a black hole with electric char
ge. Under the present experimental bound of the cosmological constant,
implications for cosmology as st straight black cosmic string are als
o discussed in comparison with a global U(1) cosmic string in the spac
etime of the zero cosmological constant. [S0556-2821(97)02324-2].