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Universal covering spaces and fundamental groups in algebraic geometry as schemes
algebraic geometry fundamental groups
2015/7/14
In topology, the notions of the fundamental group
and the universal cover are closely intertwined. By importing
usual notions from topology into the algebraic and arithmetic setting, we construct a ...
MURPHY’S LAW IN ALGEBRAIC GEOMETRY: BADLY-BEHAVED DEFORMATION SPACES
LAW IN ALGEBRAIC GEOMETRY DEFORMATION SPACES
2015/7/14
We consider the question: “How bad can the deformation space of an object
be?” The answer seems to be: “Unless there is some a priori reason otherwise, the deformation space may be as bad as possible...
Quaternionic Grassmannians and Pontryagin classes in algebraic geometry
Quaternionic Grassmannians Pontryagin classes algebraic geometry
2010/11/9
The quaternionic Grassmannian HGr(r,n) is the affine open subscheme of the ordinary Grassmannian parametrizing those 2r-dimensional subspaces of a 2n-dimensional symplectic vector space on which the ...
Topological expansion of beta-ensemble model and quantum algebraic geometry in the sectorwise approach
Topological expansion of beta-ensemble model quantum algebraic geometry sectorwise approach
2010/12/14
We solve the loop equations of the β-ensemble model analogously to the solution found for the Hermitian matrices β = 1. For β = 1, the solution was expressed using the algebraic spectral curve of equa...
ALGEBRAIC-GEOMETRY FOUNDATION FOR CONSTRUCTING SMOOTH INTERPOLANTS ON CURVED SIDES ELEMENT
2007/12/11
The aim of this paper is to lay a algebraic geometry foundation for
constructing smoothing interpolants on curved side element.
Some interpolation theorems in polynomial space are given. The main re...