Cinzia Casagrande- Fano 4-Folds With B2 Greater Than 12 Are Products of Surfaces

Explore a mathematical lecture on smooth, complex Fano 4-folds and their second Betti numbers. Delve into the theorem stating that Fano 4-folds with a second Betti number exceeding 12 are products of del Pezzo surfaces. Examine the proof, which involves a detailed analysis of divisorial elementary contractions and their exceptional divisors. Learn about the conditions under which the image of the exceptional divisor is a smooth del Pezzo surface, with its anticanonical divisor determined by the restriction of the anticanonical divisor of the target space. Gain insights into the speaker's previous work on Fano 4-folds and its relevance to this result.