1,721,078 research outputs found
On semistable principal bundles on complex projective manifolds
No full textLet be a simple linear algebraic group defined over
the field of complex numbers. Fix a proper parabolic subgroup
of , and also fix a nontrivial
antidominant character of . We prove that a holomorphic
principal --bundle over a
connected complex projective manifold is semistable
satisfying the condition that the second Chern class
vanishes
if and only if the line bundle over defined by
is numerically effective. Also, a
principal --bundle over
is semistable with if and only if for
every pair of the form
, where is a holomorphic map
to from a compact connected Riemann surface ,
and for every holomorphic reduction of structure group
to the subgroup ,
the line bundle over associated to
the principal --bundle for
is of nonnegative degree. Therefore,
is semistable with if and
only if for each pair of the above type the
--bundle over is semistable.
Similar results remain valid for principal
bundles over with a reductive linear
algebraic group as the
structure group. These generalize an earlier work of
Y. Miyaoka, \cite{Mi}, where he gave a characterization
of semistable vector bundles over a smooth projective curve.
Using these characterizations one can also
produce similar criteria for the semistability of parabolic
principal bundles over a compact Riemann surface
Holomorphic Cartan geometry on manifolds with numerically effective tangent bundle
No full textAbstractLet X be a compact connected Kähler manifold such that the holomorphic tangent bundle TX is numerically effective. A theorem of Demailly et al. (1994) [11] says that there is a finite unramified Galois covering M→X, a complex torus T, and a holomorphic surjective submersion f:M→T, such that the fibers of f are Fano manifolds with numerically effective tangent bundle. A conjecture of Campana and Peternell says that the fibers of f are rational and homogeneous. Assume that X admits a holomorphic Cartan geometry. We prove that the fibers of f are rational homogeneous varieties. We also prove that the holomorphic principal G-bundle over T given by f, where G is the group of all holomorphic automorphisms of a fiber, admits a flat holomorphic connection
Theta Functions and Projective Structures
No full textGiven a compact Riemann surface , we consider the line, in the space of holomorphic sections of on , orthogonal to all the sections that vanish at the origin. This line produces a natural meromorphic bidifferential on with a pole of order two on the diagonal. This bidifferential is extensively investigated. In particular we show that it produces a projective structure on , which is different from the standard ones
Higgs bundles and fundamental group schemes
Full text linkRelying on a notion of ``numerical effectiveness'' for Higgs bundles, we show that the category of ``numerically flat'' Higgs vector bundles on a smooth projective variety is a Tannakian category. We introduce the associated group scheme, that we call the ``Higgs fundamental group scheme of ,'' and show that its properties are related to a conjecture about the vanishing of the Chern classes of numerically flat Higgs vector bundles
On semistable principal bundles on complex projective manifolds, II
No full textLet be a compact connected K\"ahler manifold of complex dimension and a holomorphic principal --bundle, where is a connected reductive linear algebraic group defined over . Let denote the center of . We prove that the
following three statements are equivalent:
\begin{enumerate} \item{} There is a parabolic subgroup and a holomorphic reduction of structure group
to , such that the corresponding --bundle
admits a unitary flat connection, where is the Levi quotient of .
\item{} The adjoint vector bundle is numerically flat.
\item{} The principal --bundle is pseudostable, and
\end{enumerate}
If is a complex projective manifold, and represents a rational cohomology class, then the third statement is equivalent to the statement that is semistable with
Going Beyond Counting First Authors in Author Co-citation Analysis
Full text linkThe 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
Full text link“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
Full text linkWe 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
Dispelling the Myths Behind First-author Citation Counts
Full text linkWe conducted a full-scale evaluative citation analysis study of scholars in the XML research field to explore just how different from each other author rankings resulting from different citation counting methods actually are, and to demonstrate the capability of emerging data and tools on the Web in supporting more realistic citation counting methods. Our results contest some common arguments for the continued
use of first-author citation counts in the evaluation of scholars, such as high correlations between author rankings by first-author citation counts and other citation
counting methods, and high costs of using more realistic citation counting methods that are not well-supported by the ISI databases. It is argued that increasingly available digital full text research papers make it possible for citation analysis studies to go beyond what the ISI databases have directly supported and to employ more
sophisticated methods
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