Toric varieties with huge Grothendieck group

Details Toric varieties with huge Grothendieck group Toric varieties with huge Grothendieck group

2002-03-11

arxiv.org/abs/math/0203095v3

Mathematics

Algebraic Geometry

Final version, to appear in Advances in Mathematics

Scientific paper

In each dimension n>2 there are many projective simplicial toric varieties
whose Grothendieck groups of vector bundles are at least as big as the ground
field. In particular, the conjecture that the Grothendieck groups of locally
trivial sheaves and coherent sheaves on such varieties are rationally
isomorphic fails badly.

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