Smooth and irreducible multigraded Hilbert schemes
Algebraic Geometry
2010-03-15 v2 Commutative Algebra
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.
Cite
@article{arxiv.0811.3594,
title = {Smooth and irreducible multigraded Hilbert schemes},
author = {Diane Maclagan and Gregory G. Smith},
journal= {arXiv preprint arXiv:0811.3594},
year = {2010}
}
Comments
added references, corrected typos, and made minor improvements to the exposition