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Semantic communication (SemCom) and edge computing are two disruptive solutions to address emerging requirements of huge data communication, bandwidth efficiency and low latency data processing in Metaverse. However, edge computing resources are often provided by computing service providers and thus it is essential to design appealingly incentive mechanisms for the provision of limited resources. Deep learning (DL)- based auction has recently proposed as an incentive mechanism that maximizes the revenue while holding important economic properties, i.e., individual rationality and incentive compatibility. Therefore, in this work, we introduce the design of the DLbased auction for the computing resource allocation in SemComenabled Metaverse. First, we briefly introduce the fundamentals and challenges of Metaverse. Second, we present the preliminaries of SemCom and edge computing. Third, we review various incentive mechanisms for edge computing resource trading. Fourth, we present the design of the DL-based auction for edge resource allocation in SemCom-enabled Metaverse. Simulation results demonstrate that the DL-based auction improves the revenue while nearly satisfying the individual rationality and incentive compatibility constraints.