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math.AG2002
Multigraded Hilbert Schemes
Mark Haiman, Bernd Sturmfels
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 con…
math.AG2000
Hilbert schemes, polygraphs, and the Macdonald positivity conjecture
Mark Haiman
We study the isospectral Hilbert scheme X_n, defined as the reduced fiber product of C^2n with the Hilbert scheme H_n of points in the plane, over the symmetric power S^n C^2. We p…