Smooth and irreducible multigraded Hilbert schemes

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

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

References in corpus (1)

• Hilbert schemes of 8 points

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