This paper introduces the Chinese Essay Argument Mining Corpus (CEAMC), a manually annotated dataset designed for argument component classification on multiple levels of granularity. Existing argument component types in education remain simplistic and isolated, failing to encapsulate the complete argument information. Originating from authentic examination settings, CEAMC categorizes argument components into 4 coarse-grained and 10 fine-grained delineations, surpassing previous simple representations to capture the subtle nuances of argumentation in the real world, thus meeting the needs of complex and diverse argumentative scenarios. Our contributions include the development of CEAMC, the establishment of baselines for further research, and a thorough exploration of the performance of Large Language Models (LLMs) on CEAMC. The results indicate that our CEAMC can serve as a challenging benchmark for the development of argument analysis in education.