$K$-theory of cones of smooth varieties

Details $K$-theory of cones of smooth varieties $K$-theory of cones of smooth varieties

2009-05-28

arxiv.org/abs/0905.4642v2

Mathematics

K-Theory and Homology

17 pages

Scientific paper

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 $K_0(R)$ and $K_1(R)$, and prove that $K_{-1}(R)=\oplus H^1(C,\cO(n))$. The formula for $K_0(R)$ involves the Zariski cohomology of twisted K\"ahler differentials on the variety.

Affiliated with

Also associated with

No associations

Rating

$K$-theory of cones of smooth varieties does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with $K$-theory of cones of smooth varieties, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and $K$-theory of cones of smooth varieties will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-294011