Smooth and Irreducible Multigraded Hilbert schemes

Diane Maclagan (University of Warwick)

Monday 3rd November, 2008 16:00-17:00 Mathematics Building, room 416


The multigraded Hilbert scheme parameterizes all ideals in a multigraded polynomial ring with a given Hilbert function, or equivalently all G-invariant subschemes Z of affine space for which H^0(O_Z) is a fixed representation of G, where G is an abelian group. These encompass many known variants of Hilbert schemes. When Haiman and Sturmfels introduced the multigraded Hilbert schemes, they conjectured that they are always smooth and irreducible when the polynomial ring has two variables. I will discuss joint work with Greg Smith where we prove this conjecture. No background on Hilbert schemes will be assumed.

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