Around the Mukai conjecture for Fano manifolds

Kento Fujita

Around the Mukai conjecture for Fano manifolds

Algebraic Geometry 2015-04-03 v2

Authors: Kento Fujita

Abstract

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

Keywords

Mukai conjecture Fano manifolds Picard number index classification

Cite

@article{arxiv.1409.8433,
  title  = {Around the Mukai conjecture for Fano manifolds},
  author = {Kento Fujita},
  journal= {arXiv preprint arXiv:1409.8433},
  year   = {2015}
}

Comments

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

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