Journal of Algebraic Geometry

Journal of Algebraic Geometry

Online ISSN 1534-7486; Print ISSN 1056-3911

   
 
 

 

Multigraded Hilbert schemes


Authors: Mark Haiman and Bernd Sturmfels
Journal: J. Algebraic Geom. 13 (2004), 725-769
DOI: https://doi.org/10.1090/S1056-3911-04-00373-X
Published electronically: March 15, 2004
MathSciNet review: 2073194
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Abstract | References | Additional Information

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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Additional Information

Mark Haiman
Affiliation: Department of Mathematics, University of California, Berkeley, California 94720

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

DOI: https://doi.org/10.1090/S1056-3911-04-00373-X
Received by editor(s): June 10, 2002
Published electronically: 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

American Mathematical Society