Nash Problem for quotient surface singularities

We give an affirmative answer to Nash Problem for quotient surface singularities, in particular for the icosahedral singularity $E_8$.Comment: 25 pages with 5 figures. This is part of the author\'s PhD thesi

Business-Science Research Collaboration under Moral Hazard

I analyze, in the context of business and science research collaboration, how the characteristics of partnership agreements are the result of an optimal contract between partners. The final outcome depends on the structure governing the partnership, and on the informational problems towards the efforts involved. The positive effect that the effort of each party has on the success of the other party, makes collaboration a preferred solution. Divergence in research goals may, however, create conflicts between partners. This paper shows how two different structures of partnership governance (a centralized, and a decentralized ones) may optimally use the type of project to motivate the supply of non-contractible efforts. Decentralized structure, however, always choose a project closer to its own preferences. Incentives may also come from monetary transfers, either from partners sharing each other benefits, or from public funds. I derive conditions under which public interventiocollaboration, basic research, applied research, project, firms, universities, partnership governance

Irreducibility of analytic arc-sections of hypersurface singularities

We explore the existence of irreducible and reducible arc-sections in an irreducible hypersurface singularity germ along finite projections. In particular we provide examples of irreducible isolated hypersurface singularities for which no irreducible arc-sections exist, and show that reducible ones always exist. Moreover, we give an algorithm to check if a given projection allows irreducible arc-sections, and find them if they exist.Comment: 13 pages, 2 figure

Chinchillidae and Dolichotinae rodents (Rodentia: Hystricognathi: Caviomorpha) from the late Pleistocene of Southern Brazil

New records of rodents from the late Pleistocene Chuí Creek, Rio Grande do Sul State, southern Brazil, are here described. A partial dentary with fragmented cheek teeth is identified as Chinchillidae, Lagostomus Brookes cf. L. maximus (Desmarest). Other two specimens are identified as cheek teeth of Dolichotinae indet. (Caviidae). Pleistocene fossils of Lagostomus were previously reported for Argentina and Uruguay. The material of Lagostomus from Chuí Creek represents the first confidently record of this taxon Brazil. Pleistocene fossil remains of Dolichotinae have been found in Argentina, Uruguay and other areas of southern Brazil, though the Brazilian find lack precise stratigraphic information. These new records widen the paleobiogeographic distribution of Lagostomus and confirm the presence of Dolichotinae during the late Pleistocene of southern Brazil.Fil: Kerber, Leonardo. Fundação Zoobotânica do Rio Grande do Sul; BrasilFil: Pereira Lopes, Renato. Universidade Federal do Rio Grande do Sul; BrasilFil: Vucetich, María Guiomar. Universidad Nacional de La Plata. Facultad de Ciencias Naturales y Museo. División Paleontología Vertebrados; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - La Plata; ArgentinaFil: Ribeiro, Ana Maria. Fundação Zoobotânica do Rio Grande do Sul; BrasilFil: Pereira, Jamil. Museu Coronel Tancredo Fernandes de Mello; Brasi

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