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The Local Structure of Compactified Jacobians: Deformation Theory
Compactified Jacobian compactified Picard scheme nodal curve torsion-free sheaf
2011/9/16
Abstract: This paper studies the local geometry of compactified Jacobians constructed by Caporaso, Oda-Seshadri, Pandharipande, and Simpson. The main result is a presentation of the completed local ri...
Local structure of the set of steady-state solutions to the 2D incompressible Euler equations
Local structure of the set steady-state solutions 2D incompressible Euler equations
2011/1/21
It is well known that the incompressible Euler equations can be formulated in a very geometric language. The geometric structures provide very valuable insights into the properties of the solutions.
On the local structure and the homology of CAT$(\kappa)$ spaces and euclidean buildings
local structure CAT$(\kappa)$ spaces euclidean buildings
2010/12/7
We prove that every open subset of a euclidean building is a finite dimensional absolute neighborhood retract. This implies in particular that such a set has the homotopy type of a finite dimensional ...
Local Structure of Moduli Spaces
boundedness connections differential operators good quotients
2010/12/3
We provide a sketch of the GIT construction of the moduli spaces for the three classes of connections: the class of meromorphic connections with fixed divisor of poles D and its subclasses of integrab...
On a Local Structure in Kaplansky Algebras. Definitions and Basic Properties
Haussdorf projective limits C-algebras AW-algebras
2011/2/25
We introduce and study locally AW-algebras (Baer locally C-algebras) as a locally multiplicatively convex generalization of AW-algebras of Kaplansky. Among other basic properties of these algebras.