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

...tics may refer to two different formulae in [[differential geometry]] or [[algebraic topology]]. ==Cartan formula in differential geometry== ...

In [[algebraic topology]] and [[algebraic geometry]], '''Leray's theorem''' (so named after [[Jean Leray]]) relates abstract [ ...}) = 0</math> for all <math>i \ge 1</math> and all <math> U_1, \dots, U_p \in \mathcal{U})</math>, then ...

...on for a [[rational surface]]. Let ''S'' be an algebraic surface that is [[Algebraic curve#Singularities|non-singular]] and projective. Suppose there is a morph *[[List of complex and algebraic surfaces]] ...

[[:Category:Geometry|Geometry]] | [[:Category:Algebraic geometry|Algebraic&nbsp;geometry]] | ...

* [[Riemann–Hurwitz formula]] in algebraic geometry ...

...eber's theorem''', named after [[Heinrich Martin Weber]], is a result on [[algebraic curve]]s. It states the following. * {{cite book | author=Coolidge, J. L. | title=A Treatise on Algebraic Plane Curves | location=New York | publisher=Dover | page=135 | year=1959 | ...

...n|When differentials on an algebraic surface represent as a pullback of an algebraic curve}} ...plex [[algebraic surface]]s. Let ''X'' be such a surface, projective and [[Algebraic curve#Singularities|non-singular]], and let ...

{{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}} ...

...)|signature]] of the [[intersection theory|intersection pairing]] on the [[algebraic curve]]s ''C'' on ''V''. It says, roughly speaking, that the space spanned ...H'' be the [[divisor class]] on ''V'' of a [[hyperplane section]] of ''V'' in a given [[projective embedding]]. Then the intersection ...

...ann surface]]s, or, more generally, [[algebraic curve]]s, ''X'' and ''Y'', in the case of [[genus (mathematics)|genus]] ''g'' > 1. The simplest is that t ...renced as the De Franchis-[[Francesco Severi|Severi]] theorem. It was used in an important way by [[Gerd Faltings]] to prove the [[Mordell conjecture]]. ...

...am Fulton (mathematician)|William Fulton]] and Johan Hansen, who proved it in 1979. The formal statement is that if ''V'' and ''W'' are irreducible algebraic subvarieties of a [[projective space]] ''P'', all over an [[algebraically c ...

...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 ...

...complex number]]s, amongst [[compact space|compact]] [[Kähler manifold]]s. In effect it says precisely which [[complex manifold]]s are defined by [[homog ...d ''M'', with a '''Hodge metric''', meaning that the [[cohomology class]] in degree 2 defined by the [[Kähler form]] ω is an ''integral'' cohomology cla ...

...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. ...

{{short description|Type of algebraic variety}} ...|Y}} the [[Product (category theory)|projection]] [[Regular map (algebraic geometry)|morphism]] ...

...o [[Function of several complex variables|several complex variables]], and in the general development of [[sheaf cohomology]]. Theorem B is stated in cohomological terms (a formulation that Cartan ([[#CITEREFCartan1953|1953]] ...

{{short description|Number of connected components an algebraic curve can have}} ...s of the degree of the curve. For any algebraic curve of degree {{mvar|m}} in the real [[projective plane]], the number of components {{mvar|c}} is bound ...

{{short description|Theorem stating that smooth algebraic curve has minimum genus its homology class}} In [[mathematics]], a smooth [[algebraic curve]] <math>C</math> in the [[complex projective plane]], of degree <math>d</math>, has [[Genus_(ma ...

...r an [[algebraically closed field]] ''K''. Given functions ''f'' and ''g'' in ''K''(''C''), i.e. rational functions on ''C'', then ...is the [[divisor (algebraic geometry)|divisor]] of the function ''h'', or in other words the [[formal sum]] of its zeroes and poles counted with [[Multi ...