Generalized Mukai conjecture for special Fano varieties

By M. Andreatta, Elena Chierici, Gianluca Occhetta. 2003

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Let X be a Fano variety of dimension n, pseudoindex iX and Picard number ρX. A generalization of a conjecture of Mukai says that ρX(iX−1)≤n. We prove that the conjecture holds for a variety X of pseudoindex iX≥n+3/3 if X admits an unsplit covering family of rational curves; we also prove that this condition is satisfied if ρX> and either X has a fiber type extremal contraction or has not small extremal contractions. Finally we prove that the conjecture holds if X has dimension five.

Subfields: Discrete Mathematics and Combinatorics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/bcca2025b9fe3722026eeff795e1248866724906