K-theoretic defect in Chern class identity for a free divisor

2016/12/22 by Liao, Xia
#Algebraic Geometry (math.AG) #FOS: Mathematics

paper · doi:10.48550/arxiv.1612.07810

Abstract

Let X be a nonsingular variety defined over an algebraically closed field of characteristic 0, and D be a free divisor. We study the motivic Chern class of D in the Grothendieck group of coherent sheaves G₀(X), and another class defined by the sheaf of logarithmic differentials along D. We give explicit calculations of the difference of these two classes when: D is a divisor on a nonsingular surface; D is a hyperplane arrangement whose affine cone is free.

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