Abstract
We show that the Hilbert scheme, that parametrizes all ideals with the same Hilbert function over an exterior algebra, is connected. We give a new proof of Hartshorne’s Theorem that the classical Hilbert scheme is connected. More precisely: if Q Q is either a polynomial ring or an exterior algebra, we prove that every two strongly stable ideals in Q Q with the same Hilbert function are connected by a sequence of binomial Gröbner deformations.
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