Zilber–Pink conjecture for Picard numbers in Lefschetz pencils
Let Y→P1\mathcal{Y}\to\mathbb{P}^1Y→P1 be a Lefschetz pencil of degree-ddd surfaces in P3\mathbb{P}^3P3. Picard-number finiteness conjecture. If d≥5d\geq 5d≥5, the Picard number of…