Smooth and irreducible multigraded Hilbert schemes

Mathematics – Algebraic Geometry

Scientific paper

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added references, corrected typos, and made minor improvements to the exposition

Scientific paper

10.1016/j.aim.2009.10.003

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 ZZ[x,y], which establishes a conjecture of Haiman and
Sturmfels.

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