K-theory of cones of smooth varieties, by Guillermo Cortiñas, Christian Haesemeyer, Mark E. Walker, and Chuck Weibel

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 give formulas for K₀(R) and K₁(R) in terms of the Zariski cohomology of twisted Kähler differentials on the variety. We also prove that K_-1(R) is the direct sum of the cohomology groups H¹(C,O(t)).

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