5 problems

Let $X$ be a smooth Fano variety. Denote by $\rho_X$ its Picard number, by $\iota_X$ its pseudo-index, and by $\dim X$ its dimension. The generalised Mukai conjecture. … with equal…

Gongyo's Mukai-type conjecture.

Let $X$ be a smooth Fano variety. Let $\rho_X$ denote its Picard number and let $\iota_X$ denote its pseudo-index, defined by … Here $-K_X$ is the anticanonical divisor of $X$. The…

Fix $n$ and $\rho\geq 2$. Let $(X,D)$ be an $n$-dimensional log Fano manifold, meaning that $X$ is smooth projective, $D$ is a reduced simple normal crossing divisor, and…

Let $X$ be a complex $n$-dimensional Fano manifold with Picard number ${\rho}_X$. For every extremal ray $R$ of $X$, define its length by … Let $l_X$ be the minimum of $l(R)$ over…