Positivity of Δ-genera for connected polarized demi-normal schemes

2017/09/21 by Chen, Jingshan, Chen, Yongchang
#14C20(Primary) #14J10(Secondary) #Algebraic Geometry (math.AG) #FOS: Mathematics

paper · doi:10.48550/arxiv.1709.07398

Abstract

In this paper, we show that the Δ-genus Δ(X,L)≥ 0 for any connected polarized demi-normal scheme (X,L). As an application, we obtain Δ(X,I(K_X+Λ))≥ 0 for any KSBA stable log scheme (X,Λ), where I is the Cartier index of K_X+Λ. We also construct examples of KSBA stable log schemes with I=1 and Δ(X,K_X+Λ)= 0, which shows the inequality is sharp when I=1.

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