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Explore the fundamental concepts of birational geometry in this specialized mathematics lecture delivered in Portuguese by Carolina Araujo. Delve into the evolution of pair theory in algebraic geometry, starting from Iitaka's program of the 1970s which focused on classifying open varieties through compactification. Learn how open varieties U are studied by compactifying them into projective varieties X with boundary divisors D, forming pairs (X,D). Examine the historical developments in pair theory, including hyperbolicity concepts, before focusing on Calabi-Yau pairs. Discover a new framework, developed collaboratively with Alessio Corti and Alex Massarenti, that provides explicit descriptions of Calabi-Yau pairs' birational geometry. Part of the Monthly Lecture Series "On the Geometry of the Cotangent Bundle and Hyperbolicity," this advanced mathematical discussion offers valuable insights into modern algebraic geometry.
