Higher Fano Manifolds in Algebraic Geometry

Explore the fascinating world of higher Fano manifolds in this 52-minute lecture by Carolina Araujo from the Instituto Nacional de Matemática Pura e Aplicada. Delve into the realm of algebraic geometry, where Fano manifolds are complex projective manifolds with positive first Chern class. Discover how this condition relates to positive curvature in differential geometry and its significant geometric and arithmetic implications. Learn about recent efforts to define suitable higher analogues of the Fano condition and their expected stronger properties. Survey the theory of higher Fano manifolds, defined by the positivity of higher Chern characters. Gain insights into recent collaborative research on homogeneous and toric higher Fano manifolds, conducted with Roya Beheshti, Ana-Maria Castravet, Kelly Jabbusch, Svetlana Makarova, Enrica Mazzon, and Nivedita Viswanathan.