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. 
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