Algebraic geometry
•
Projective geometry
Algebraic variety
In mathematics, algebraic varieties (also called varieties) are one of the central objects of study in algebraic geometry. Classically, an algebraic variety was defined to be the set of solutions of a...
Algebraic variety - Wikipedia
Algebraic manifold
•
Algebraic curve
•
Algebraic group
•
Algebraic surface
•
Birational geometry
•
Geometry of divisors
•
Quadrics
•
3-fold
Algebraic manifold
In mathematics, an algebraic manifold is an algebraic variety which is also a manifold. As such, algebraic manifolds are a generalisation of the concept of smooth curves and surfaces defined by polyno...
Algebraic curve
In mathematics, an algebraic curve or plane algebraic curve is the set of points on the Euclidean plane whose coordinates are zeros of some polynomial in two variables.For example, the unit circle is ...
Algebraic curve - Wikipedia
Algebraic group
In algebraic geometry, an algebraic group (or group variety) is a group that is an algebraic variety, such that the multiplication and inversion operations are given by regular functions on the variet...
Algebraic surface
In mathematics, an algebraic surface is an algebraic variety of dimension two. In the case of geometry over the field of complex numbers, an algebraic surface has complex dimension two (as a complex m...
Birational geometry
In algebraic geometry, the goal of birational geometry is to determine when two algebraic varieties are isomorphic outside lower-dimensional subsets. This amounts to studying mappings that are given b...
Geometry of divisors
Quadrics
Quadrics - Wikipedia
3-fold
In algebraic geometry, a 3-fold or threefold is a 3-dimensional algebraic variety.The Mori program showed that 3-folds have minimal models.
Quasi-split group
Singular point of an algebraic variety
In the mathematical field of algebraic geometry, a singular point of an algebraic variety V is a point P that is 'special' (so, singular), in the geometric sense that at this point the tangent space a...
Oblate spheroid
An oblate spheroid is a rotationally symmetric ellipsoid having a polar axis shorter than the diameter of the equatorial axis. Oblate spheroids are contracted along a line, whereas prolate spheroids a...
Jacobian variety
In mathematics, the Jacobian variety J(C) of a non-singular algebraic curve C of genus g is the moduli space of degree 0 line bundles. It is the connected component of the identity in the Picard group...
Elliptic rational functions
In mathematics the elliptic rational functions are a sequence of rational functions with real coefficients. Elliptic rational functions are extensively used in the design of elliptic electronic filter...
Elliptic rational functions - Wikipedia
Algebraic geometry of projective spaces
Projective space plays a central role in algebraic geometry. The aim of this article is to define the notion in terms of abstract algebraic geometry and to describe some basic uses of projective space...
Algebraic geometry of projective spaces - Wikipedia
Quasiprojective variety
In mathematics, a quasi-projective variety in algebraic geometry is a locally closed subset of a projective variety, i.e., the intersection inside some projective space of a Zariski-open and a Zariski...
Compact Riemann surface
In mathematics, a compact Riemann surface is a complex manifold of dimension one that is a compact space.
Riemann surfaces are generally classified first into the compact (those that are closed ma...
Exceptional divisor
In mathematics, specifically algebraic geometry, an exceptional divisor for a regular map of varieties is a kind of 'large' subvariety of which is 'crushed' by , in a certain definite sense. More str...
Complete variety
In mathematics, in particular in algebraic geometry, a complete algebraic variety is an algebraic variety X, such that for any variety Y the projection morphismis a closed map, i.e. maps closed sets ...
Severi–Brauer variety
Irreducible component
In mathematics, and specifically in algebraic geometry, the concept of irreducible component is used to make formal the idea that a set such as defined by the equationis the union of the two linesand ...
Zariski surface
In algebraic geometry, a branch of mathematics, a Zariski surface is a surface over a field of characteristic p > 0 such that there is a dominant inseparable map of degree p from the proj...
Koras–Russell cubic threefold
In algebraic geometry, the Koras–Russell cubic threefolds are smooth affine contractible threefolds studied by Koras & Russell (1997) that have a hyperbolic action of a one-dimensional torus...
Paraboloid
In mathematics, a paraboloid is a quadric surface of special kind. There are two kinds of paraboloids: elliptic and hyperbolic.The elliptic paraboloid is shaped like an oval cup and can have a maximum...
Paraboloid - Wikipedia
Burkhardt quartic
In mathematics, the Burkhardt quartic is a quartic threefold in 4-dimensional projective space studied by Burkhardt (1890, 1891, 1892), with the maximum possible number of 45 nodes.The equations ...
Kodaira dimension
In algebraic geometry, the Kodaira dimension κ(X) (or canonical dimension) measures the size of the canonical model of a projective variety X.Igor Shafarevich introduced an important numerical invaria...
Horrocks–Mumford bundle
Barth–Nieto quintic
In algebraic geometry, the Barth–Nieto quintic is a quintic 3-fold in 4 (or sometimes 5) dimensional projective space studied by Barth & Nieto (1994) that is the Hessian of the Segre cubic. The B...
Field with one element
In mathematics, the field with one element is a suggestive name for an object that should behave similarly to a finite field with a single element, if such a field could exist. This object is denoted ...
Seshadri constant
In algebraic geometry, a Seshadri constant is an invariant of an ample line bundle L at a point P on an algebraic variety. It was introduced by Demailly to measure a certain rate of growth, of the ten...
Squircle
A squircle is a mathematical shape with properties between those of a square and those of a circle. It is a special case of superellipse. The word "squircle" is a portmanteau of the words "square" an...
Squircle - Wikipedia