Around the Mukai conjecture for Fano manifolds

Kento Fujita

Published 2014-09-30Version 1

As a generalization of the Mukai conjecture, we conjecture that the Fano manifolds $X$ which satisfy the property $\rho_X(\iota_X-1)\geq\dim X-1$ have very special structure, where $\rho_X$ is the Picard number of $X$ and $\iota_X$ is the pseudoindex of $X$. In this paper, we classify those $X$ if $\rho_X\leq 3$ or $\dim X\leq 5$.