Multigraded Hilbert Schemes

Mark Haiman; Bernd Sturmfels

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Multigraded Hilbert Schemes

Mark Haiman·Bernd Sturmfels

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Abstract

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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Mark Haiman, Bernd Sturmfels. 2002-01-28. Multigraded Hilbert Schemes. https://arxiv.org/abs/math/0201271

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