On a generalization of the Mukai conjecture for Fano fourfolds

2012/06/10 by Fujita, Kento · 1 citation
#14E30 #14J35 #14J45 #Algebraic Geometry (math.AG) #FOS: Mathematics

paper · doi:10.48550/arxiv.1206.1990

Abstract

Let X be a complex Fano manifold of dimension n. Let s(X) be the sum of l(R)-1 for all the extremal rays of X, the edges of the cone NE(X) of curves of X, where l(R) denotes the minimum of (-K_X ⋅ C) for all rational curves C whose class [C] belongs to R. We show that s(X)≤ n if n≤ 4. And for n≤ 4, we completely classify the case the equality holds. This is a refinement of the Mukai conjecture on Fano fourfolds.

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