K-theory of cones of smooth varieties

2009/05/28 by Cortiñas, Guillermo, Haesemeyer, Christian, Walker, Mark E. +1 · 1 citation
#Algebraic Geometry (math.AG) #FOS: Mathematics #K-Theory and Homology (math.KT)

paper · doi:10.48550/arxiv.0905.4642

Abstract

Let R be the homogeneous coordinate ring of a smooth projective variety X over a field \k of characteristic~0. We calculate the K-theory of R in terms of the geometry of the projective embedding of X. In particular, if X is a curve then we calculate K₀(R) and K₁(R), and prove that K_-1(R)=⊕ H¹(C,\cO(n)). The formula for K₀(R) involves the Zariski cohomology of twisted Kähler differentials on the variety.

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