Multigraded Hilbert Schemes

Details Multigraded Hilbert Schemes Multigraded Hilbert Schemes

2002-01-28

arxiv.org/abs/math/0201271v1

Mathematics

Algebraic Geometry

34 pages

Scientific paper

We introduce the multigraded Hilbert scheme, which parametrizes all homogeneous ideals with fixed Hilbert function in a polynomial ring that is graded by any abelian group. Our construction is widely applicable, it provides explicit equations, and it allows us to prove a range of new results, including Bayer's conjecture on equations defining Grothendieck's classical Hilbert scheme and the construction of a Chow morphism for toric Hilbert schemes.

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