mathematics, the cone of curves (sometimes the Kleiman-Mori cone) of an algebraic variety X {\displaystyle X} is a combinatorial invariant of importance to...

the cone of curves may be spanned by one (−2)-curve and one curve with self-intersection 0.) So the cone of curves is either the standard round cone, or...

variety X, the cone of curves means the convex cone spanned by all curves in X (in the real vector space N 1 ( X ) {\displaystyle N_{1}(X)} of 1-cycles modulo...

Cone cells or cones are photoreceptor cells in the retinas of vertebrates' eyes. They respond differently to light of different wavelengths, and the combination...

degree on every curve in the variety. The classes of nef line bundles are described by a convex cone, and the possible contractions of the variety correspond...

through time as seen externally. A closed timelike curve can be created if a series of such light cones are set up so as to loop back on themselves, so it...

the curve is called a parametrization, and the curve is a parametric curve. In this article, these curves are sometimes called topological curves to distinguish...

In special and general relativity, a light cone (or "null cone") is the path that a flash of light, emanating from a single event (localized to a single...

conjecture on curves, named after Masayoshi Nagata, governs the minimal degree required for a plane algebraic curve to pass through a collection of very general...

contribute to the development of the Minimal model program (MMP). In 1984 he published a paper titled On the closed cone of curves of algebraic 3-folds where...

the curve. The requirements of regularity and nondegeneracy of Σ {\displaystyle \Sigma } ensure that closed causal curves (such as those consisting of a...

descriptions, which can all be proved to define exactly the same curves. One description of a parabola involves a point (the focus) and a line (the directrix)...

n} .) The first key result is the cone theorem of Shigefumi Mori, describing the structure of the cone of curves of X {\displaystyle X} . Briefly, the...

section, conic or a quadratic curve is a curve obtained from a cone's surface intersecting a plane. The three types of conic section are the hyperbola...

In linear algebra, a cone—sometimes called a linear cone for distinguishing it from other sorts of cones—is a subset of a vector space that is closed under...

and as a cone in drawings with one spatial dimension suppressed. time-like curves, with a speed less than the speed of light. These curves must fall...

"Hilbert's 14th problem over finite fields and a conjecture on the cone of curves", Compositio Mathematica, 144 (5): 1176–1198, arXiv:0808.0695, doi:10...

Given the problem of the aerodynamic design of the nose cone section of any vehicle or body meant to travel through a compressible fluid medium (such...

considered only for real curves, although they also make sense when defined in this way for curves over an arbitrary field. A plane curve of degree n intersects...

curves) Crunode Curve Curve sketching Jacobian variety Klein quartic List of curves Hilbert's sixteenth problem Cubic plane curve Hyperelliptic curve...

only if L has positive degree on every nonzero element C of the closure of the cone of curves NE(X) in N 1 ( X ) {\displaystyle N_{1}(X)} . (This is slightly...

forms a curve and the other sheet is a surface * For cones, cylinders, tori and cyclides both sheets form curves. * For the sphere the center of every osculating...

management, the cone of uncertainty describes the evolution of the amount of best case uncertainty during a project. At the beginning of a project, comparatively...

Journal of the Acoustical Society of America. Fletcher–Munson curves have been superseded and incorporated into newer standards. The definitive curves are...

bevel gear, is the angle between face cone and pitch cone. The addendum circle coincides with the tops of the teeth of a gear and is concentric with the standard...

definitions for a tangent cone, including the adjacent cone, Bouligand's contingent cone, and the Clarke tangent cone. These three cones coincide for a convex...

strain can be determined (see tensile testing). These curves reveal many of the properties of a material, such as the Young's modulus, the yield strength...

developable of a smooth curve in space. A ruled surface can be described as the set of points swept by a moving straight line. For example, a cone is formed...

Traffic cones, also called pylons, witches' hats, road cones, highway cones, safety cones, caution cones, channelizing devices, construction cones, roadworks...

cutting of a right circular cone by a plane perpendicular to an element of the cone. That is, Menaechmus is reputed to have discovered the curves that were...