nonsingular geometry

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• Minimal model (birational geometry) — In algebraic geometry, more specifically in the field of birational geometry, the theory of minimal models is part of the birational classification of algebraic varieties. Its goal is to construct, given a variety satisying certain restrictions,… …   Wikipedia

• Metric tensor — In the mathematical field of differential geometry, a metric tensor is a type of function defined on a manifold (such as a surface in space) which takes as input a pair of tangent vectors v and w and produces a real number (scalar) g(v,w) in a… …   Wikipedia

• Resolution of singularities — Strong desingularization of Observe that the resolution does not stop after the first blowing up, when the strict transform is smooth, but when it is simple normal crossings with the exceptional divisors. In algebraic geometry, the problem of… …   Wikipedia

• Curve — For other uses, see Curve (disambiguation). A parabola, a simple example of a curve In mathematics, a curve (also called a curved line in older texts) is, generally speaking, an object similar to a line but which is not required to be straight.… …   Wikipedia

• Oval (projective plane) — In mathematics, an oval in a projective plane is a set of points, no three collinear, such that there is a unique tangent line at each point (a tangent line is defined as a line meeting the point set at only one point, also known as a 1 secant).… …   Wikipedia

• Algebraic curve — In algebraic geometry, an algebraic curve is an algebraic variety of dimension one. The theory of these curves in general was quite fully developed in the nineteenth century, after many particular examples had been considered, starting with… …   Wikipedia

• Collineation — In projective geometry, a collineation is a one to one and onto map (a bijection) from one projective space to another, or from a projective space to itself, such that the images of collinear points are themselves collinear. All projective linear …   Wikipedia

• Toric variety — In algebraic geometry, a toric variety or torus embedding is a normal variety containing an algebraic torus as a dense subset, such that the action of the torus on itself extends to the whole variety. Contents 1 The toric variety of a fan 2… …   Wikipedia

• Elliptic curve — In mathematics, an elliptic curve is a smooth, projective algebraic curve of genus one, on which there is a specified point O . An elliptic curve is in fact an abelian variety mdash; that is, it has a multiplication defined algebraically with… …   Wikipedia

• Trott curve — In real algebraic geometry, the Trott curve is the set of points ( x , y ) satisfying the degree four polynomial equation:displaystyle 144(x^4+y^4) 225(x^2+y^2)+350x^2y^2+81=0.These points form a nonsingular quartic plane curve that has genus… …   Wikipedia

• Cross-ratio — D is the harmonic conjugate of C with respect to A and B In geometry, the cross ratio, also called double ratio and anharmonic ratio, is a special number associated with an ordered quadruple of collinear points, particularly points on a… …   Wikipedia