Non-coherent Components of the Toric Hilbert Scheme

Details Non-coherent Components of the Toric Hilbert Scheme Non-coherent Components of the Toric Hilbert Scheme

2010-09-22

arxiv.org/abs/1009.4321v1

Mathematics

Algebraic Geometry

34 pages, 2 figures

Scientific paper

We want to understand the geometry of all irreducible components of the toric Hilbert scheme. Until now it is known that the coherent component is (up to normalisation) the toric variety associated to the state polytope of the toric ideal. For the non-coherent components it was only known that there exists such a polytope describing the normalisation. Using the local equations and various facts about toric Hilbert schemes, we will derive an explicit construction of the polytope corresponding to the normalisation of the underlying reduced structure of a given non-coherent component of the toric Hilbert scheme.

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