Codimension Two Determinantal Varieties with Isolated Singularities

We study codimension two determinantal varieties with isolated singularities. These singularities admit a unique smoothing, thus we can define their Milnor number as the middle Betti number of their generic fiber. For surfaces in C^4, we obtain a L\^e-Greuel formula expressing the Milnor number of the surface in terms of the second polar multiplicity and the Milnor number of a generic section. We also relate the Milnor number with Ebeling and Gusein-Zade index of the 1- form given by the differential of a generic linear projection defined on the surface. To illustrate the results, in the last section we compute the Milnor number of some normal forms from A. Fr\"uhbis-Kr\"uger and A. Neumer [2] list of simple determinantal surface singularities

On a generic symmetry defect hypersurface

We show that symmetry defect hypersurfaces for two generic members of the irreducible algebraic family of n-dimensional smooth irreducible subvarieties in general position in C²ⁿ are homeomorphic and they have homeomorphic sets of singular points. In particular symmetry defect curves for two generic curves in C² of the same degree have the same numer of singular points

On a singular variety associated to a polynomial mapping from \C^n to \C^{n-1}

We construct a singular variety ${\mathcal{V}}_G$ associated to a polynomial mapping G : \C^{n} \to \C^{n - 1} where $n \geq 2$. We prove that in the case G : \C^{3} \to \C^{2}, if $G$ is a local submersion but is not a fibration, then the homology and the intersection homology with total perversity (with compact supports or closed supports) in dimension two of the variety ${\mathcal{V}}_G$ is not trivial. In the case of a local submersion G : \C^{n} \to \C^{n - 1} where $n \geq 4$, the result is still true with an additional condition

On the simplicity of multigerms

We prove several results regarding the simplicity of germs and multigerms obtained via the operations of augmentation, simultaneous augmentation and concatenation and generalised concatenation. We also give some results in the case where one of the branches is a non stable primitive germ. Using our results we obtain a list which includes all simple multigerms from $\mathbb C^3$ to $\mathbb C^3$.Comment: 26 pages, to appear in Mathematica Scandinavica. Second version adds two families that were missing in Table

Carl Einstein Interdisciplinar : sobre "Escultura Negra" ("Negerplastik")

With "Negerplastik" ("Escultura Negra" in portuguese) the Santa Catarina University Press publishes the first book by Carl Einstein (1885-1940) edited in Brazil. In this context and doing justice to the nowadays important relation between art and political action, this article presents information in multidisciplinary perspective about the artist/writer, the translation of "Negergebet" and "Drei Negerlieder", considering the relevance of African arts and literature in Einstein's work, as well as a reading guide tuned and useful in order to understand his work.A Editora da UFSC publica o ensaio "Negerplastik" ("Escultura Negra") de Carl Einstein (1885-1940), autor até então inédito no Brasil. No ensejo e em vista da premência atual do vínculo arte e ação política, este artigo apresenta informações multidisciplinares referentes à atuação do escritor/artista, inclusive a tradução para o português da "Negergebet" ("Prece Africana") e das "Drei Negerlieder" ("Três Canções Africanas") devidas à relevância da literatura e das artes africanas no trabalho legado por Einstein, bem como um mapa de leituras afinadas e úteis à compreensão de seu trabalho.Mit "Negerplastik" ("Escultura Negra" auf Portugiesisch) stellt der Verlag der Bundesuniversität von Santa Catarina die erste in Brasilien veröffentlichte Arbeit Carl Einsteins (1885-1940) vor. Aus diesem Anlass und um die heute als vorrangig empfundene Beziehung zwischen Kunst und politischer Aktion Rechnung zu tragen, stellt dieser Artikel multidisziplinär hergeleitete Informationen über Carl Einstein zur Verfügung - nebst der portugiesischen Übersetzung von "Negergebet" ("Prece Africana") und "Drei Negerlieder" ("Três Canções Africanas"). Dies geschieht angesichts der Bedeutung von Literatur und afrikanischer Kunst im Werk Einsteins, deren Beziehung sich durch diese Informationen eher erschliessen mag

Os verbos "ser" e "estar" em oposição ao verbo "sein" do alemão

People who learn Portuguese usually have difficulties in using two of the most frequent verbs of the Portuguese verbal system: ser and estar. Native speakers of German for example fail to easily identify the differences between these verbs, which are compared with the German verb sein. Our purpose is to describe these verbs, their meaning and function, and also to attempt to find criteria to help learners to identify the differences to use these verbs. Some of the differences can be explained by the speakers experiences and the context.Lerner des Portugiesischen als Fremdsprache haben oft Schwierigkeiten, die zwei häufig gebrauchten Verben des portugiesischen Verbalsystems ser und estar zu verwenden. Deutschsprachige erkennen kaum die Unterschiede zwischen diesen Verben, die im Deutschen oft mit dem Verb sein gleichgesetzt werden, das auch in ähnlichen Strukturen und Situationen vorkommt. In dieser Arbeit beschäftigen wir uns damit, diese Verben in ihrer Funktion und Bedeutung zu beschreiben und versuchen, Kriterien aufzustellen, die dem Lernenden helfen können, diese Unterschiede besser zu verstehen und dadurch die Verben besser anzuwenden. Einige Unterschiede können durch die Erfahrungen des Sprechers und durch den Kontext erklärt werden

Feminismo insurgente: mantenimiento del sujeto colectivo

Artigo apresentado como trabalho de conclusão do curso de Especialização em Relações Internacionais Contemporâneas.La conversión de la guerrilla de las FARC en partido político evidenció el modelo colectivo adoptado en el proceso de paz en Colombia. Sin embargo, el mantenimiento de la colectividad en el actual proceso de implementación del Acuerdo de Final ha sufrido retrocesos. En un rol clave como constructoras de la paz, las mujeres farianas crearon el Feminismo Insurgente con el objetivo de eliminar la cultura patriarcal y todas las formas de discriminación. El pensar colectivo del Feminismo Insurgente mantiene vivo el ideario colectivo creado al interior de las filas guerrilleras entre hombre y mujeres, luego puede ser explorado como una herramienta de manutención de la colectividad entre los excombatientes en la vida civil. Así, como propuesta de remediar os efectos del enflaquecimiento de la colectividad entre los excombatientes, este trabajo tiene como finalidad reflexionar sobre el quehacer del Feminismo Insurgente en la etapa de implementación del Acuerdo Final