Journal of Algebraic Geometry

Author(s): Mark Haiman; Bernd Sturmfels
Journal: J. Algebraic Geom. 13 (2004), 725-769.
Posted: March 15, 2004
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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
Affiliation: Department of Mathematics, University of California, Berkeley, California 94720

Bernd Sturmfels
Affiliation: Department of Mathematics, University of California, Berkeley, California 94720

PII: S 1056-3911(04)00373-X
Received by editor(s): June 10, 2002
Posted: March 15, 2004
Additional Notes: The first author's research was supported in part by NSF grant DMS-0070772. The second author's research was supported in part by NSF grant DMS-9970254

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