Singularities and holonomicity of binomial D-modules

We study binomial D-modules, which generalize A-hypergeometric systems. We determine explicitly their singular loci and provide three characterizations of their holonomicity. The first of these is an equivalence of holonomicity and L-holonomicity for these systems. The second refines the first by giving more detailed information about the L-characteristic variety of a non-holonomic binomial D-module. The final characterization states that a binomial D-module is holonomic if and only if its corresponding singular locus is proper.