[permalink] [id link]

Every algebraic curve C of genus g ≥ 1 is associated with an abelian variety J of dimension g, by means of an analytic map of C into J.

from
Wikipedia

## Some Related Sentences

Every and algebraic

__Every__field has

**an**

__algebraic__extension which

**is**algebraically closed ( called its

__algebraic__closure ), but proving this in general requires some form

**of**the axiom

**of**choice

**.**

__Every__epimorphism in this

__algebraic__sense

**is**

**an**epimorphism in the sense

**of**category theory

**,**but the converse

**is**not true in all categories

**.**

*

__Every__root**of**a monic polynomial whose coefficients are__algebraic__integers**is**itself**an**__algebraic__integer**.**__Every__

__algebraic__structure has its own notion

**of**homomorphism

**,**namely any function compatible

**with**the operation ( s ) defining the structure

**.**

*

__Every__nonempty affine__algebraic__set may be written uniquely as a union**of**__algebraic__varieties ( where none**of**the sets in the decomposition are subsets**of**each other ).
*

__Every__holomorphic vector bundle on a projective**variety****is**induced**by**a unique__algebraic__vector bundle**.**
*

__Every__real__algebraic__number field K**of**degree n contains a PV number**of**degree n**.**This number**is**a field generator**.**
*

__Every__substructure**is**the union**of**its finitely generated substructures ; hence Sub ( A )**is****an**__algebraic__lattice**.**
Also

**,**a kind**of**converse holds:__Every____algebraic__lattice**is**isomorphic to Sub ( A ) for some algebra A**.**
*

__Every__character value**is**a sum**of**n m < sup > th </ sup > roots**of**unity**,**where n**is**the degree ( that**is****,**the**dimension****of**the**associated**vector space )**of**the representation**with**character χ and m**is**the order**of****g****.**In particular**,**when F**is**the field**of**complex numbers**,**every such character value**is****an**__algebraic__integer**.**
* Let K < sup > a </ sup > be

**an**__algebraic__closure**of**K containing L**.**__Every__embedding σ**of**L in K < sup > a </ sup > which restricts to the identity on K**,**satisfies σ ( L ) = L**.**In other words**,**σ**is****an**automorphism**of**L over K**.**__Every__

__algebraic__plane

**curve**has a degree

**,**which can be defined

**,**in case

**of**

**an**algebraically closed field

**,**as number

**of**intersections

**of**the

**curve**

**with**a generic line

**.**

__Every__planar graph has

**an**

__algebraic__dual

**,**which

**is**in general not unique ( any dual defined

**by**a plane embedding will do ).

Every and curve

*

__Every__quadratic Bézier__curve__**is**also a cubic Bézier__curve__**,**and more generally**,**every degree n Bézier__curve__**is**also a degree m__curve__for any m > n**.**In detail**,**a degree n__curve__**with**control points P < sub > 0 </ sub >, …, P < sub > n </ sub >**is**equivalent ( including the parametrization ) to the degree n +**1**__curve__**with**control points P '< sub > 0 </ sub >, …, P '< sub > n +**1**</ sub >, where**.**__Every__point on the Lorenz

__curve__represents a statement like " the bottom 20 %

**of**all households have 10 %

**of**the total income

**.**

__Every__study has found that instead

**of**people's MBTI scores clustering around two opposite poles

**,**such as intuition vs

**.**sensation

**,**

**with**few people scoring in the middle

**,**people's scores actually cluster around the middle

**of**each scale in a bell

__curve__

**.**

__Every__closed

__curve__c on X

**is**homologous to for some simple closed curves c < sub > i </ sub >, that

**is**

**,**

__Every__minimal projective ruled surface other than the projective plane

**is**the projective bundle

**of**a 2-dimensional vector bundle over some

__curve__

**.**

Every and C

__Every__character

**is**automatically continuous from A to

__C__

**,**since the kernel

**of**a character

**is**a maximal ideal

**,**which

**is**closed

**.**

__Every__continuous

**map**f: X → Y induces

**an**algebra homomorphism

__C__( f ):

__C__( Y ) →

__C__( X )

**by**the rule

__C__( f )( φ ) = φ o f for every φ in

__C__( Y ).

Also among the early 32 members were syndicated panel cartoonists Dave Breger ( Mister Breger ), George Clark ( The Neighbors ), Bob Dunn ( Just the Type ) and Jimmy Hatlo ( They'll Do It

__Every__Time ); freelance magazine cartoonists Abner Dean and Mischa Richter**,**editorial cartoonists Rube Goldberg ( New York Sun ), Burris Jenkins ( New York Journal American ),__C__**.**D**.**Batchelor ( Daily News ) and Richard Q**.**Yardley ( The Baltimore Sun ); sports cartoonist Lou Hanlon ; illustrator Russell Patterson and comic book artists Joe Shuster and Joe Musial**.**
*

__Every__separable metric space**is**isometric to a subset**of**__C__(), the separable Banach space**of**continuous functions → R**,****with**the supremum norm**.**__Every__year since 1982

**,**the W

**.**

__C__

**.**Handy Music Festival

**is**held in the Florence / Sheffield / Muscle Shoals area

**,**featuring blues

**,**jazz

**,**country

**,**gospel

**,**rock music and R & B

**.**

According to Canon

__C__**.**24**,**"__Every__priest having a cure**of**souls shall provide that**,**in the absence**of**reasonable hindrance**,**Morning and Evening Prayer daily and on appointed days the Litany shall be said in the church**,**or one**of**the churches**,****of**which he**is**the minister**.**
" Canon

__C__**.**26 stipulates that "__Every__clerk ( cleric ) in Holy Orders**is**under obligation**,**not being let ( prevented )**by**sickness or some other urgent cause**,**to say daily the Morning and Evening Prayer ...." In other Anglican provinces**,**the Daily Office**is**not a canonical obligation but**is**strongly encouraged**.**
*

__Every__cover**is**a local homeomorphism — that**is****,**for every**,**there exists a neighborhood**of**c and a neighborhood**of**such that the restriction**of**p to U yields a homeomorphism from U to V**.**This implies that__C__and X share all local properties**.**__Every__fall

**,**FRC Action ( the political action group affiliated

**with**FRC ) holds

**an**annual summit composed for conservative Christian activists and evangelical voters in Washington

**,**D

**.**

__C__

**.**

This

**means**that A**is**not necessarily better than B**,**and B**is**not necessarily better than__C__**.**__Every__class**is**independent**of**the others**.**
*

__Every__finite-dimensional simple algebra over R must be a matrix ring over R**,**__C__**,**or H**.**__Every__central simple algebra over R must be a matrix ring over R or H**.**These results follow from the Frobenius theorem**.**
*

__Every__finite-dimensional simple algebra over__C__must be a matrix ring over__C__and hence every central simple algebra over__C__must be a matrix ring over__C__**.**0.933 seconds.