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This paper is an exposition on how Grothendieck’s Quot scheme
can be seen as a solution to the moduli problem of quotient sheaves. These
schemes as corresponding moduli spaces play a significant role, not only
in solving problems within geometry in general, but they are also applicable to problems of classification in algebra. These Quot schemes are introduced in context of the setting up of a solution to a moduli problem. This is
then followed by its application to particular problems of classifying continuously varying families of quotient sheaves with a fixed Hilbert polynomial. The purpose of this investigation is to bridge the often abstract
settings of moduli theory as pioneered by Grothendieck, and its concrete
application through solving particular moduli problems in concrete projective geometric setting. In particular, this study will present how algebraic geometry through moduli theory helps reveal significant information
about the family of objects which it parameterizes.
Hafiz Syed Husaina, Mariam Sultana. (2020) Grothendieck’s Quot Scheme and Moduli of Quotient Sheaves, Punjab University Journal of Mathematics, Volume 52 , Issue No.4.
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