ACM sets of points in multiprojective space
Elena Guardo, Adam Van Tuyl (2008)
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Elena Guardo, Adam Van Tuyl (2008)
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Daniel Katz, Javid Validashti (2010)
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Juan C. Migliore (2006)
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A great deal of recent activity has centered on the question of whether, for a given Hilbert function, there can fail to be a unique minimum set of graded Betti numbers, and this is closely related to the question of whether the associated Hilbert scheme is irreducible or not. We give a broad class of Hilbert functions for which we show that there is no minimum, and hence that the associated Hilbert sheme is reducible. Furthermore, we show that the Weak Lefschetz Property holds for the...
Runar Ile (2007)
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Maps between deformation functors of modules are given which generalise the maps induced by the Knörrer functors. These maps become isomorphisms after introducing certain equations in the target functor restricting the Zariski tangent space. Explicit examples are given on how the isomorphisms extend results about deformation theory and classification of MCM modules to higher dimensions.
Anthony Vito Geramita, Brian Harbourne, Juan Migliore (2009)
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Christopher Stuart (2007)
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In this note an internal property of a ring of sets, named the Nested Partition Property, is shown to imply the Nikodym Property. A wide range of examples are shown to have this property.
Lorenzo Robbiano (2009)
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Martin Kreuzer, Lorenzo Robbiano (2008)
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Francesca Cioffi, Maria Grazia Marinari, Luciana Ramella (2009)
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Montsserrat Teixidor i Bigas (2007)
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We show that the moduli space of coherent systems of rank two and dimension four on a generic curve of genus at least two is non-empty for any value of the parameter when the Brill-Noether number is at least one and the degree is odd or when the Brill-Noether number is at least ve and the degree is even. In all these cases there is one component of the moduli space of coherent systems of the expected dimension. The case of rank two and dimension four is particularly relevant as it is...