Complex sentence: It is most convenient to choose J with special properties, such as nongeneric symmetries or integrability, so computations are often carried out on Kähler manifolds using the techniques of algebraic geometry.
Split into simpler sentences: It is most convenient to choose J with special properties, such as nongeneric symmetries or integrability. Computations are often carried out on Kähler manifolds using the techniques of algebraic geometry.