The Hilbert scheme of the Grassmannian is not connected

摘要

We show that whend >= 3,the Hilbert schemeHilbdT+1-(d-12)(G(k,n))has 2 connected components, even though elements in both components have the same cohomology class. Moreover, we show that the Hilbert scheme associated to the Hilbert polynomial(T+mm)-(T+m-dm)in Grassmannian has at most 2 connected components. Communicated by Lawrence Ein