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Most research on abstractive summarization focuses on single-domain applications, often neglecting how domain shifts between documents affect performance and the generalization ability of summarization models. To address this issue, we introduce DomainSum, a hierarchical benchmark designed to capture fine-grained domain shifts in abstractive summarization. We categorize these shifts into three levels: genre, style, and topic, and demonstrate through comprehensive benchmark analysis that they follow a hierarchical structure. Furthermore, we evaluate the domain generalization capabilities of commonly used pre-trained language models (PLMs) and large language models (LLMs) in both in-domain and cross-domain settings. Our benchmark and source code are released at https://github.com/hpzhang94/DomainSum.