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)).

Guillermo Cortiñas <gcorti@dm.uba.ar>
Christian Haesemeyer <chh@math.ucla.edu>
Mark E. Walker <mwalker5@math.unl.edu>
Chuck Weibel <weibel@math.rutgers.edu>