Search for dissertations about: "Hilbert scheme"
Showing result 1 - 5 of 10 swedish dissertations containing the words Hilbert scheme.
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1. Families of cycles and the Chow scheme
Abstract : The objects studied in this thesis are families of cycles on schemes. A space — the Chow variety — parameterizing effective equidimensional cycles was constructed by Chow and van der Waerden in the first half of the twentieth century. Even though cycles are simple objects, the Chow variety is a rather intractable object. READ MORE
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2. Hilbert schemes and Rees algebras
Abstract : The topic of this thesis is algebraic geometry, which is the mathematical subject that connects polynomial equations with geometric objects. Modern algebraic geometry has extended this framework by replacing polynomials with elements from a general commutative ring, and studies the geometry of abstract algebra. READ MORE
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3. Compactifying locally Cohen-Macaulay projective curves
Abstract : We define a moduli functor parametrizing finite maps from a projective (locally) Cohen-Macaulay curve to a fixed projective space. The definition of the functor includes a number of technical conditions, but the most important is that the map is almost everywhere an isomorphism onto its image. READ MORE
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4. Moduli spaces of zero-dimensional geometric objects
Abstract : The topic of this thesis is the study of moduli spaces of zero-dimensional geometricobjects. The thesis consists of three articles each focusing on a particular moduli space.The first article concerns the Hilbert scheme Hilb(X). This moduli space parametrizesclosed subschemes of a fixed ambient scheme X. READ MORE
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5. The space of Cohen–Macaulay curves and related topics
Abstract : The space of Cohen–Macaulay curves is a compactification of the space of curves that are embedded in a given projective space Pn. The idea is similar to that of the Hilbert scheme but instead of adding degenerated curves, one considers only curves without embedded or isolated points. READ MORE
