Grading of the affine line and its Quot scheme
Abstract: For a field kand a grading of the polynomial ringk[t]with Hilbert functionh, weconsider the Quot functor QuothV , where V = ? di =1k[t]is a finitely generated and free k[t]-module. The Quot functor parametrizes, for any k-algebra B, homogeneous B [t]-submodulesN⊆B⊗kVsuch that the graded components of the quotient( B⊗kV)/Nare locally freeB-modules of rank given byh. We find that it is locallyrepresentable by a polynomial ring over kin a finite number of variables. Finally, weshow that there is a scheme that represents the Quot functor that is both smooth and irreducible.
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