Multigraded Hilbert schemes
- Author(s): Haiman, Mark
- Sturmfels, B
- et al.
Published Web Locationhttp://www.ams.org/distribution/jag/2004-13-04/S1056-3911-04-00373-X/home.html
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.