Birational geometry of Deligne-Mumford stacks

Key Points

• To explore birational geometry specifically in the context of Deligne-Mumford stacks and introduce new invariants.
• Investigation of the structure and properties of Deligne-Mumford stacks.
• Definition of novel birational invariants relevant to these stacks.
• New birational invariants are defined that enhance understanding of Deligne-Mumford stacks.
• Insights into how these invariants relate to the geometry of the stacks are provided.