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In [[mathematics]], '''Chow's theorem''' may refer to a number of theorems due to [[Wei-Liang Chow]]: ...lytic geometry#Chow's theorem|Chow's theorem]]: Any analytic subvariety in projective space is actually algebraic. ...

...ism φ from ''S'' to the [[projective line]], with ''general fibre'' also a projective line. Then the theorem states that ''S'' is rational.<ref>{{cite journal | [[Category:Theorems in algebraic geometry]] ...

...am Fulton (mathematician)|William Fulton]] and Johan Hansen, who proved it in 1979. ...t is that if ''V'' and ''W'' are irreducible algebraic subvarieties of a [[projective space]] ''P'', all over an [[algebraically closed field]], and if ...

...sor product]]s of [[module (mathematics)|modules]]|Homological conjectures in commutative algebra}} ...t also be incident. An intersection theorem is not necessarily true in all projective geometries; it is a property that some geometries satisfy but others don't. ...

{{short description|Characterises non-singular projective varieties amongst compact Kähler manifolds}} ...complex number]]s, amongst [[compact space|compact]] [[Kähler manifold]]s. In effect it says precisely which [[complex manifold]]s are defined by [[homog ...

...ription|The 3 long diagonals of a hexagon tangent to a conic section meet in a single point}} ...n]], its principal [[diagonal]]s (those connecting opposite vertices) meet in a single point. It is named after [[Charles Julien Brianchon]] (1783–1864). ...

...fication of [[Regular curve|regular curves]] in space up to [[Translation (geometry)|translation]] and [[rotation]]. ...as a stepping stone to a larger result, rather than as a useful statement in-and-of itself. ...

...erential geometry]] topics. See also [[glossary of differential and metric geometry]] and [[list of Lie group topics]]. ==Differential geometry of curves and surfaces== ...

{{short description|Result that expresses a function f(x + y) in terms of f(x) and f(y)}} {{About|addition theorems in general|specific addition theorems for trigonometric functions|angle addition formulas}} ...

...athematics]], a smooth [[algebraic curve]] <math>C</math> in the [[complex projective plane]], of degree <math>d</math>, has [[Genus_(mathematics)#Topology|genus ...math> is any smoothly embedded connected curve representing the same class in [[homology (mathematics)|homology]] as <math>C</math>, then the genus <math ...

In [[mathematics]], the '''Hodge index theorem''' for an [[algebraic surface]] ...divisor class]] on ''V'' of a [[hyperplane section]] of ''V'' in a given [[projective embedding]]. Then the intersection ...

The theorem was proved in the case of projective planes by {{Harvtxt|Bruck|Ryser|1949}}. It was extended to symmetric design == Projective planes == ...

...|Y}} the [[Product (category theory)|projection]] [[Regular map (algebraic geometry)|morphism]] ...s can be seen as an analogue of [[Compact space|compactness]] in algebraic geometry: a [[topological space]] {{mvar|X}} is compact if and only if the above pro ...

...n [[Moritz Pasch]],<ref>{{Harvnb|Pasch|1912}}</ref> is a result in [[plane geometry]] which cannot be derived from [[Euclid's postulates]]. ...var|b}}, {{mvar|d}}).<ref>{{harvtxt|Coxeter|1969|p=179}} states the result in 12.274 but does not refer to it specifically as Pasch's theorem.</ref>}} [H ...

...are the curves.<ref>James S. Milne, ''Jacobian Varieties'', Corollary 12.2 in {{Harvtxt|Cornell|Silverman|1986}}</ref> ...rieties]], is [[injective]] (on [[geometric point]]s). Generalizations are in two directions. Firstly, to geometric questions about that morphism, for ex ...

...cal result on complex [[algebraic surface]]s. Let ''X'' be such a surface, projective and [[Algebraic curve#Singularities|non-singular]], and let ...ation|title=Geometry and Complex Variables|volume=132|series=Lecture Notes in Pure and Applied Mathematics|first=S.|last=Coen|publisher=CRC Press|year=19 ...

...for example, two distinct projective lines in a [[projective plane]] meet in exactly one point (there is no "parallel" case). ...]]. This definition is a special instance of the general definition of a [[projective space]]. ...

{{short description|Relates the geometric vector bundles to algebraic projective modules}} ...odule]]s and gives rise to a common intuition throughout [[mathematics]]: "projective modules over [[commutative ring]]s are like vector bundles on [[compact spa ...

...' is a basic result of [[complex manifold]] theory and complex [[algebraic geometry]], describing general conditions under which [[sheaf cohomology]] groups wi ...sation, the [[Nakano vanishing theorem|Kodaira–Nakano vanishing theorem]], in which <math>K_M\otimes L\cong\Omega^n(L)</math>, where Ω^''n''('' ...

...e of the curve. For any algebraic curve of degree {{mvar|m}} in the real [[projective plane]], the number of components {{mvar|c}} is bounded by ...is [[Singularity theory|nonsingular]]. Moreover, any number of components in this range of possible values can be attained. ...