Around the Mukai conjecture for Fano manifolds

Kento Fujita

paper

Around the Mukai conjecture for Fano manifolds

arXiv:1409.8433

Abstract

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

21 pages, minor revision; modify Theorem 1.6, add Section 8 and references