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Construction Of Quot-Schemes, Majid Dehghani

Electronic Theses and Dissertations

The Quot Scheme is a construction representing parameter spaces for quotient objects of sheaves or coherent modules over a scheme. It encapsulates families of quotients by fixing a certain quotient's structure. The Hilbert Scheme, a specific type of Quot Scheme, focuses on parameterizing subschemes of a fixed projective space by fixing their Hilbert polynomials. After recalling the basic concepts of the theory, we explain the Grothendieck’s Quot scheme construction and its Grassmannian embedding. Then we continue to an explicit construction of Quot scheme in the case of graded modules over graded rings.