Learning representations of entity mentions is a core component of modern entity linking systems for both candidate generation and making linking predictions. In this paper, we present and empirically analyze a novel training approach for learning mention and entity representations that is based on building minimum spanning arborescences (i.e., directed spanning trees) over mentions and entities across documents to explicitly model mention coreference relationships. We demonstrate the efficacy of our approach by showing significant improvements in both candidate generation recall and linking accuracy on the Zero-Shot Entity Linking dataset and MedMentions, the largest publicly available biomedical dataset. In addition, we show that our improvements in candidate generation yield higher quality re-ranking models downstream, setting a new SOTA result in linking accuracy on MedMentions. Finally, we demonstrate that our improved mention representations are also effective for the discovery of new entities via cross-document coreference.