Following the recent exploration of smooth heterotic compactifications with
unitary bundles, orbifold compactifications in six dimensions can be shown to
correspond in the blow-up to compactifications with U(1) gauge backgrounds. A
powerful tool is the comparison of anomaly polynomials. The presentation here
focuses on heterotic SO(32) compactifications in six dimensions including
five-branes. Four dimensional and E8 x E8 models are briefly commented on.Comment: Submitted for the SUSY07 proceedings, 4 pages, LaTe