Second Chern class of Fano manifolds and anti-canonical geometry

2017/10/11 by Liu, Jie · 1 citation
#14C20 #14J30 #14J35 #14J45 #Algebraic Geometry (math.AG) #FOS: Mathematics

paper · doi:10.48550/arxiv.1710.04116

Abstract

Let X be a Fano manifold of Picard number one. We establish a lower bound for the second Chern class of X in terms of its index and degree. As an application, if Y is a n-dimensional Fano manifold with -K_Y=(n-3)H for some ample divisor H, we prove that h⁰(Y,H)≥ n-2. Moreover, we show that the rational map defined by \vert mH\vert is birational for m≥ 5, and the linear system \vert mH\vert is basepoint free for m≥ 7. As a by-product, the pluri-anti-canonical systems of singular weak Fano varieties of dimension at most 4 are also investigated.

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• Degrees of non-Gorenstein canonical Fano threefolds with Picard number one

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