Although there is a rich body of research on dependency theory, only few results concerning
simple functional dependencies (FDs) have been published. In this paper, the following key results ...regarding simple FDs are shown. First, given an acyclic set
F of simple FDs there exists exactly one canonical cover for
F. Second, this uniquely determined canonical cover can be computed via transitive reduction. Third, it is shown how a uniquely determined canonical cover can be fixed in case of arbitrary simple FDs via transitive reduction.
This paper presents new examples of projective surfaces of general type over C$\mathbb {C}$ with canonical map of degree 3 onto a surface of general type. Very few examples are known of such surfaces ...and some of the examples in this paper present the new feature of having the canonical map not a morphism (i.e. the canonical linear system with base points).
Given a nowheredense closed subset X of a metrizable compact space X˜, we characterize the dimension of X in terms of the multiplicity of the canonical covers of the complementary of X, especially in ...some particular cases, like when X˜ is the Hilbert cube or the finite dimensional cube and X, a Z-set of X˜. In this process, we solve some related questions in the literature.
In this article we study the bicanonical map φ₂ of quadruple Galois canonical covers X of surfaces of minimal degree. We show that φ₂ has diverse behavior and exhibits most of the complexities that ...are possible for a bicanonical map of surfaces of general type, depending on the type of X. There are cases in which φ₂ is an embedding, and if it so happens, φ₂ embeds X as a projectively normal variety, and there are cases in which φ₂ is not an embedding. If the latter, φ₂ is finite of degree 1, 2 or 4. We also study the canonical ring of X, proving that it is generated in degree less than or equal to 3 and finding the number of generators in each degree. For generators of degree 2 we find a nice general formula which holds for canonical covers of arbitrary degrees. We show that this formula depends only on the geometric and the arithmetic genus of X.
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