Smooth and irreducible multigraded Hilbert schemes |
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| Authors: | Diane Maclagan |
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| Institution: | a Mathematics Institute, University of Warwick, Coventry, CV4 7AL, United Kingdom
b Department of Mathematics & Statistics, Queen's University, Kingston, ON, K7L 3N6, Canada |
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| Abstract: | The multigraded Hilbert scheme parametrizes all homogeneous ideals in a polynomial ring graded by an abelian group with a fixed Hilbert function. We prove that any multigraded Hilbert scheme is smooth and irreducible when the polynomial ring is Zx,y], which establishes a conjecture of Haiman and Sturmfels. |
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| Keywords: | Hilbert schemes Multigraded rings Combinatorial commutative algebra |
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