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Explore a lecture by Bruno de Oliveira from the University of Miami that introduces the canonical model singularities (CMS) criterion for determining the bigness of cotangent bundles for surfaces. Learn about invariants for canonical singularities, with specific formulas provided for A_n singularities. Discover how the CMS-criterion leads to conjectures and insights regarding the geography and possible ratios of c_1^2/c_2 for surfaces with big cotangent bundles. The lecture distinguishes between regular and irregular surfaces, demonstrating how the CMS-criterion can be applied to show the existence of deformations of hypersurfaces in P³ with big cotangent bundles for degree d≥8. Examine examples of regular surfaces with big cotangent bundles having ratios close to 1/5, and irregular surfaces with ratios approaching 1/5. Time permitting, the discussion extends to ratios below 1/5.
