Around the Mukai conjecture for Fano manifolds

@article{Fujita2014AroundTM,
title={Around the Mukai conjecture for Fano manifolds},
author={K. Fujita},
journal={European Journal of Mathematics},
year={2014},
volume={2},
pages={120-139}
}
• K. Fujita
• Published 2014
• Mathematics
• European Journal of Mathematics
• As a generalization of the Mukai conjecture, we conjecture that the Fano manifolds $$X$$X which satisfy the property $$\rho _X(r_X-1)\ge \dim X-1$$ρX(rX-1)≥dimX-1 have very special structure, where $$\rho _X$$ρX is the Picard number of $$X$$X and $$r_X$$rX is the index of $$X$$X. In this paper, we classify those $$X$$X with $$\rho _X\le 3$$ρX≤3 or $$\dim X\le 5$$dimX≤5.
2 Citations