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Grading of the affine line and its Quot scheme
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.).
2011 (English)Independent thesis Advanced level (degree of Master (Two Years)), 20 credits / 30 HE creditsStudent thesis
Abstract [en]

For a field

kand a grading of the polynomial ringk[t]with Hilbert functionh, weconsider the Quot functor


, where V =



=1k[t]is a finitely generated and


k[t]-module. The Quot functor parametrizes, for any k-algebra B, homogeneous


[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.

Place, publisher, year, edition, pages
2011. , 39 p.
National Category
Engineering and Technology
URN: urn:nbn:se:kth:diva-102882OAI: diva2:557257
Educational program
Master of Science in Engineering -Engineering Physics
Available from: 2012-09-27 Created: 2012-09-27 Last updated: 2012-09-27Bibliographically approved

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