TITLE: Fundamental motivation for several complex variables
QUESTION [18 upvotes]: I have 3 general abstract reasons to care about complex analysis in a single variable:

The laplacian is, up to a constant multiple, the only isometry invariant PDO in the plane, and so it is abstractly very important.  Holomorphic functions are intimately related to harmonic functions, so holomorphic functions are important.
Holomorphic mappings are conformal if they have nonvanishing derivatives
Many results which are real variable in nature are most easily understood in the light of complex analysis (factorization of real polynomials, radius of convergence of real power series, etc)

I currently have no such justification for several complex variables.  The connection to harmonic functions mostly breaks down.  Conformality breaks down.  I have not seen applications to real variable phenomena.  
Can anyone give me some insight into the big picture here?  Where do the phenomena studied in several complex variables (domains of holomorphy and their ilk) come up in the rest of mathematics?

REPLY [7 votes]: If those are your reasons for caring about complex analysis, then I'm not sure to what extent I can convince you to care about SCV.
But here is why I like SCV: I like multivariable calculus, and I like complex numbers.  I've always wondered what would happen if you put the two together.  And apparently pretty wild things happen (compared with either the single-variable or real-variable case).
I'm also really interested in complex geometry.  The local theory of complex manifolds involves SCV.
One final comment: Your reason (1) for caring about holomorphic functions is in fact my reason for caring about harmonic functions (for which I would otherwise desire motivation).