Generalized Mukai conjecture for special Fano varieties

Authors: Marco Andreatta; Elena Chierici; Gianluca Occhetta

Source: Central European Journal of Mathematics, Volume 2, Number 2, 1 April 2004 , pp. 272-293(22)

Publisher: Central European Science Journals

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Abstract:

Let X be a Fano variety of dimension n, pseudoindex iX and Picard number rhoX. A generalization of a conjecture of Mukai says that rhoX (iX - 1) le n. We prove that the conjecture holds for a variety X of pseudoindex iX ge (n+3)/3 if X admits an unsplit covering family of rational curves; we also prove that this condition is satisfied if rhoX > 1 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.

Keywords: FANO VARIETIES; RATIONAL CURVES; MSC (2000): 14J45; 14E30

Document Type: Research article

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