1,720,957 research outputs found
Deformations and Simulatenous Resolutions of Determinantal Surfaces
Get PDFThis paper uses reconstruction algebras to construct simultaneous resolution
of determinantal surfaces. The main new difference to the classical case is
that, in addition to the quiver of the reconstruction algebra, certain
noncommutative relations, namely those of the canonical algebra of Ringel, are
required. All the relations of the reconstruction algebra except the canonical
relation are then deformed, and these deformed relations together with
variation of the GIT quotient achieve the simultaneous resolution.Comment: 14 pages. arXiv admin note: text overlap with arXiv:2208.1196
Localization in different categories
No full textA thesis submitted to the Directorate of Research and Graduate Training in partial fulfillment of the requirements for the award of the Degree of Masters of Science in Mathematics of Makerere University.Localization can be thought of as a systematic way of inverting morphisms in a category to construct a new one. This can be formulated accurately in terms of a universal property. In this study, we looked at localization in some special cases such as in a ring for both the commutative and non-commutative case, module over a commutative ring and in a more general setting, which is localization of the homotopy category of complexes to obtain the derived category. Analysis of the different localizations involved investigations into the localizing class, the universal property and Ore conditions imposed in each case and it was shown that localization has almost the same properties for different categories. An analysis in the relationship of localization in different categories was carried out to obtain the general properties such as the localizing class, Ore conditions and the universal property of localization to enable one localize an arbitrary category as provided in this study.Eastern Africa Universities Mathematics Programme (EAUMP)
Computing the Artin component using Reconstruction Algebras.
No full textA Thesis Submitted to the Directorate of Research and Graduate Training in Fulfillment of the Requirements for the Award of the Degree of Doctor of Philosophy in Mathematics of Makerere University.This thesis studies noncommutative resolutions of non-Gorenstein singularities and uses them to construct classical deformation spaces. In the first part, it recovers the Artin component of the deformation space of a cyclic surface singularity using only the quiver of the corresponding reconstruction algebra. The relations of the reconstruction algebra are then deformed, and the deformed relations together with variation of
the Geometric Invariant Theory (GIT) quotient achieve the simultaneous resolution. This extends work of Brieskorn, Kronheimer, Grothendieck, Cassens–Slodowy and Crawley-Boevey–Holland into the setting of singularities C^2/H with H \leq GL(2, C), and furthermore gives a prediction for what is true more generally.
Additionally, outside the toric setting, the thesis demonstrates the construction of simultaneous resolution for determinantal surfaces, which are a specific type of rational surface singularities. The main new difference to the above case is that, in addition to the quiver of the reconstruction algebra, certain noncommutative relations, namely those of the canonical algebra of Ringel, are required. All the relations of the reconstruction algebra except the canonical relation are then deformed, and these deformed relations together with variation of the GIT quotient achieve the simultaneous resolution.GRAID program, ERC Consolidator Grant 101001227 (MMiMMa)
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
The Artin component and simultaneous resolution via reconstruction algebras of type A
Get PDFThis paper uses noncommutative resolutions of non-Gorenstein singularities to construct classical deformation spaces by recovering the Artin component of the deformation space of a cyclic surface singularity using only the quiver of the corresponding reconstruction algebra. The relations of the reconstruction algebra are then deformed, and the deformed relations together with variation of the GIT quotient achieve the simultaneous resolution. This extends the work of Brieskorn, Kronheimer, Grothendieck, Cassens–Slodowy, and Crawley-Boevey–Holland into the setting of singularities C
2
/H with H≤GL(2,C) and furthermore gives a prediction for what is true more generally
Localization in different categories
No full textA dissertation submitted to the Directorate of Research and Graduate Training in partial fulfillment of the award of Master of Science degree in Mathematics of Makerere UniversityLocalization can be thought of as a systematic way of inverting morphisms in a category to
construct a new one. This can be formulated accurately in terms of a universal property.
In this study, we looked at localization in some special cases such as in a ring for both
the commutative and non-commutative case, module over a commutative ring and in a
more general setting, which is localization of the homotopy category of complexes to obtain
the derived category. Analysis of the diferent localizations involved investigations into the
localizing class, the universal property and Ore conditions imposed in each case and it
was shown that localization has almost the same properties for different categories. An
analysis in the relationship of localization in different categories was carried out to obtain
the general properties such as the localizing class, Ore conditions and the universal property
of localization to enable one localize an arbitrary category as provided in this study.EAUM
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
Dispelling the Myths Behind First-author Citation Counts
Get PDFWe 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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