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Each curve in this example is a locus defined as the conchoid of the point P and the line l.In this example, P is 8 cm from l. In geometry, a locus (plural: loci) (Latin word for "place", "location") is a set of all points (commonly, a line, a line segment, a curve or a surface), whose location satisfies or is determined by one or more specified conditions.
A linear system of divisors algebraicizes the classic geometric notion of a family of curves, as in the Apollonian circles.. In algebraic geometry, a linear system of divisors is an algebraic generalization of the geometric notion of a family of curves; the dimension of the linear system corresponds to the number of parameters of the family.
In analytic geometry, any equation involving the coordinates specifies a subset of the plane, namely the solution set for the equation, or locus. For example, the equation y = x corresponds to the set of all the points on the plane whose x-coordinate and y-coordinate are equal.
On the sphere, the cut locus of a point consists of the single antipodal point diametrically opposite to it. On an infinitely long cylinder, the cut locus of a point consists of the line opposite the point. Let X be the boundary of a simple polygon in the Euclidean plane. Then the cut locus of X in the interior of the polygon is the polygon's ...
Examples of the most studied classes of algebraic varieties are lines, circles, parabolas, ellipses, hyperbolas, cubic curves like elliptic curves, and quartic curves like lemniscates and Cassini ovals. These are plane algebraic curves. A point of the plane lies on an algebraic curve if its coordinates satisfy a given polynomial equation.
The set of exceptional points on is called the ramification locus (i.e. this is the complement of the largest possible open set ′). In general monodromy occurs according to the fundamental group of W ′ {\displaystyle W'} acting on the sheets of the covering (this topological picture can be made precise also in the case of a general base field).
Although the military has thrown a cloak of secrecy over its operations, the Echo Company of the Army’s 160th Special Operations Aviation Regiment is increasingly being lauded in special ...
A classic example of this is the twisted cubic in : it is a smooth local complete intersection meaning in any chart it can be expressed as the vanishing locus of two polynomials, but globally it is expressed by the vanishing locus of more than two polynomials.