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Geometric Construction Of Crystal Bases
 Duke Math. J
, 1996
"... We realize the crystal associated to the quantized enveloping algebras with a symmetric generalized Cartan matrix as a set of Lagrangian subvarieties of the cotangent bundle of the quiver variety. As a byproduct, we give a counterexample to the conjecture of KazhdanLusztig on the irreducibility o ..."
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Cited by 101 (6 self)
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We realize the crystal associated to the quantized enveloping algebras with a symmetric generalized Cartan matrix as a set of Lagrangian subvarieties of the cotangent bundle of the quiver variety. As a byproduct, we give a counterexample to the conjecture of KazhdanLusztig on the irreducibility of the characteristic variety of the intersection cohomology sheaves associated with the Schubert cells of type A and also to the similar problem asked by Lusztig on the characteristic variety of the perverse sheaves corresponding to canonical bases. 1.
Error Propagation in Geometric Constructions
, 2000
"... In this paper we consider error propagation in geometric constructions from a geometric viewpoint. First we study affine combinations of convex bodies: This has numerous examples in splines curves and surfaces defined by control points. Second, we study in detail the circumcircle of three points in ..."
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Cited by 12 (7 self)
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In this paper we consider error propagation in geometric constructions from a geometric viewpoint. First we study affine combinations of convex bodies: This has numerous examples in splines curves and surfaces defined by control points. Second, we study in detail the circumcircle of three points
Axiomatizing geometric constructions
, 2008
"... In this survey paper, we present several results linking quantifierfree axiomatizations of various Euclidean and hyperbolic geometries in languages without relation symbols to geometric constructibility theorems. Several fragments of Euclidean and hyperbolic geometries turn out to be naturally occu ..."
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Cited by 5 (0 self)
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In this survey paper, we present several results linking quantifierfree axiomatizations of various Euclidean and hyperbolic geometries in languages without relation symbols to geometric constructibility theorems. Several fragments of Euclidean and hyperbolic geometries turn out to be naturally
Tropical plane geometric constructions
, 2008
"... In this article we give a general method to compute sets of algebraic curves with prescribed incidence relations and tropicalizations. It generalizes the geometric constructions presented in Tabera, 2005 to the non linear case. ..."
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In this article we give a general method to compute sets of algebraic curves with prescribed incidence relations and tropicalizations. It generalizes the geometric constructions presented in Tabera, 2005 to the non linear case.
Exact rounding for geometric constructions
, 1997
"... Exact rounding is provided for elementary floatingpoint arithmetic operations (e.g. in the IEEE standard). Many authors have felt that it should be provided for other operations, in particular for geometric constructions. We show how one may round modular representation of numbers to the closest f ..."
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Cited by 1 (1 self)
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Exact rounding is provided for elementary floatingpoint arithmetic operations (e.g. in the IEEE standard). Many authors have felt that it should be provided for other operations, in particular for geometric constructions. We show how one may round modular representation of numbers to the closest
Elegant Geometric Constructions
 FORUM GEOM
, 2005
"... With the availability of computer software on dynamic geometry, beautiful and accurate geometric diagrams can be drawn, edited, and organized efficiently on computer screens. This new technological capability stimulates the desire to strive for elegance in actual geometric constructions. The prese ..."
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Cited by 2 (1 self)
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With the availability of computer software on dynamic geometry, beautiful and accurate geometric diagrams can be drawn, edited, and organized efficiently on computer screens. This new technological capability stimulates the desire to strive for elegance in actual geometric constructions
Geometric Constructions of Nongeometric String Theories
, 2002
"... We advocate a framework for constructing perturbative closed string compactifications which do not have largeradius limits. The idea is to augment the class of vacua which can be described as fibrations by enlarging the monodromy group around the singular fibers to include perturbative stringy dual ..."
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Cited by 125 (5 self)
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We advocate a framework for constructing perturbative closed string compactifications which do not have largeradius limits. The idea is to augment the class of vacua which can be described as fibrations by enlarging the monodromy group around the singular fibers to include perturbative stringy
Multimodal Visualization of Geometrical Constructions
"... CabriII We present an environment for multimodal visualization of geometrical constructions, including both graphical and textual realizations. The graphic interface is programmed by direct ma nipulation, and this process is mirrored in the text. The text resembles a program written in a classical ..."
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CabriII We present an environment for multimodal visualization of geometrical constructions, including both graphical and textual realizations. The graphic interface is programmed by direct ma nipulation, and this process is mirrored in the text. The text resembles a program written in a
STATISTICAL ACCURACY OF GEOMETRIC CONSTRUCTIONS
"... Abstract. In this expositorycompendium, a new approachfor assessing complexity of classical geometric constructions is presented. Everyone who has experience of making geometric constructions in practice knows how much attention must be paid to a careful placement of the compass and the straightedge ..."
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Abstract. In this expositorycompendium, a new approachfor assessing complexity of classical geometric constructions is presented. Everyone who has experience of making geometric constructions in practice knows how much attention must be paid to a careful placement of the compass
Geometrical Construction of Type I
, 1997
"... The parameterspace orbifold construction of open and unoriented toroidal and (targetspace) orbifold compactifications is briefly reviewed, with emphasis on the underlying geometrical framework. A class of chiral fourdimensional typeI vacua with three generations is also discussed. ..."
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The parameterspace orbifold construction of open and unoriented toroidal and (targetspace) orbifold compactifications is briefly reviewed, with emphasis on the underlying geometrical framework. A class of chiral fourdimensional typeI vacua with three generations is also discussed.
Results 1  10
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9,248