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Gonality, Clifford index and multisecants.
No full textAbstractThe gonality of a projective curve C is the minimal degree of a morphism f:C→P1. It is a classical invariant which has been refined by the introduction of the Clifford index. If C⊂P3 is a smooth, connected curve, Gon(C) is said to be computable by multisecants if Gon(C)=deg(C)−l where l is the highest order of a multisecant to C. In this paper we prove that the gonality is computable by multisecants and that Cliff(C)=Gon(C)−2 for most subcanonical curves in P3. We also describe the stratification by multisecants of the Hilbert schemes of complete intersections and rational curves
On subcanonical surfaces of .
No full textWe work over an algebraically closed field of characteristic zero. It is well known that the existence of indecomposable rank two vector bundles on P^n is equivalent, via the correspondance of Serre, to the existence of smooth X, of codimension two, which are subcanonical and non complete intersections. If n is at least 4, basically, only one example of non split rank two vector bundle is known: the Horrocks-Mumford bundle on P^4. This bundle is associated to a smooth abelian surface of degree ten. This surface lies on a hyperquintic. In this paper we consider the problem of the existence of smooth subcanonical surfaces in P^4 lying on hypersurfaces of degree at most 4.
If the degree of the hypersurface is 1 or 2, it is not diffcult to show that the surface is a complete intersection. Thanks to a result of Koelblen, the same conclusion holds true if the degree of the hypersurface is 3
Smooth divisors of projective hypersurfaces.
No full textWe work over an algebraically closed field of arbitrary characteristic. Ellingsrud-Peskine proved that smooth surfaces in P^4 are subject to strong limitations. Their whole argument is derived from the fact that the sectional genus of surfaces of degree d lying on a hypersurface of degree s varies in an interval of length d(s-1)^2/2s. The aim of the present paper is to show that for smooth codimension two subvarieties of P^n, n at least 5, one can get a similar result with an interval whose length depends only on s. The main point is a Lemma whose proof is a direct application of the positivity of N_X(-1) (where N_X is the normal bundle of X in P^n). As a consequence of our Lemma we get a series of (n-3) inequalities the first one of which being Lemme 1 of Ellingsrud-Peskine. The second Theorem was obtained in a preliminary version by an essentially equivalent but more geometric argument.
Then we first derive two consequences:
1) roughly speaking, the family of "biliaison classes" of smooth subvarieties of P^5 lying on a hypersurface of degree s is limited;
2) the family of smooth codimension two subvarieties of P^6 lying on a hypersurface of degree s is limited.
The result quoted in 1) is not effective, but 2) is.
In the last section we try to obtain precise inequalities connecting the usual numerical invariants of a smooth subcanonical subvariety X of P^n, n at least 5 (the degree d, the integer e such that the canonical sheaf of X is e times the hyperplane, the least degree, s, of an hypersurface containing X). In particular we prove thet s is less then or equal to n+1
Going Beyond Counting First Authors in Author Co-citation Analysis
Get PDFThe present study examines one of the fundamental aspects of author co-citation analysis (ACA) - the way co-citation
counts are defined. Co-citation counting provides the data on which all subsequent statistical analyses and mappings
are based, and we compare ACA results based on two different types of co-citation counting - the traditional type that
only counts the first one among a cited work's authors on the one hand and a non-traditional type that takes into
account the first 5 authors of a cited work on the other hand. Results indicate that the picture produced through this non-traditional author co-citation counting contains more coherent author groups and is therefore considerably clearer. However, this picture represents fewer specialties in the research field being studied than that produced through the traditional first-author co-citation counting when the same number of top-ranked authors is selected and analyzed. Reasons for these effects are discussed
Variations on the Author
Get PDF“Variations on the Author” discusses two of Eduardo Coutinho’s recent films (Um Dia na Vida, from 2010, and Últimas Conversas, posthumously released in 2015) and their contribution to the general question of documentary authorship. The director’s filmography is characterized by a consistent yet self-effacing form of authorial self-inscription: Coutinho often features as an interviewer that rather than express opinions propels discourses; an interviewer that is good at listening. This mode of self-inscription characterizes him as an author who is not expressive but who is nonetheless markedly present on the screen. In Um Dia na Vida, however, Coutinho is completely absent form the image, while Últimas Conversas, on the contrary, includes a confessional prologue that moves the director from the margins to the center of his films. This article examines the ways in which these works stand out in the filmography of a director who offers new insights into the notion of cinematic authorship
Appropriate Similarity Measures for Author Cocitation Analysis
Get PDFWe provide a number of new insights into the methodological discussion about author cocitation analysis. We first argue that the use of the Pearson correlation for measuring the similarity between authors’ cocitation profiles is not very satisfactory. We then discuss what kind of similarity measures may be used as an alternative to the Pearson correlation. We consider three similarity measures in particular. One is the well-known cosine. The other two similarity measures have not been used before in the bibliometric literature. Finally, we show by means of an example that our findings have a high practical relevance.information science;Pearson correlation;cosine;similarity measure;author cocitation analysis
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