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- Learn more:✕This summary was generated using AI based on multiple online sources. To view the original source information, use the "Learn more" links.Period (algebraic geometry) In algebraic geometry, a period is a number that can be expressed as an integral of an algebraic function over an algebraic domain. Sums and products of periods remain periods, such that the periods form a ring. Maxim Kontsevich and Don Zagier gave a survey of periods and introduced some conjectures about them.en.wikipedia.org/wiki/Period_(algebraic_geometry)Algebraic Period In algebra, a period is a number that can be written an integral of an algebraic function over an algebraic domain. More specifically, a period is a real number where is a polynomial and is a rational function on with rational coefficients.mathworld.wolfram.com/AlgebraicPeriod.htmlRoughly speaking, periods are numbers that arise as integrals of polynomial differential forms over sets that are cut out by polynomial equations. More conceptually, periods are numbers that arise from the natural pairing between singular and algebraic de Rham cohomology of varieties (or more generally, motives) over $mathbb {Q}$.www.fields.utoronto.ca/talks/Periods-algebraic-geo…Here is an elementary definition of a period: Definition 1 A period is the value of an absolutely convergent multi-variable inte-gral of a rational function with algebraic coefficients, over a domain in Rn given by polynomial inequalities with algebraic coefficients.www.ihes.fr/~maxim/TEXTS/Periods-short.pdf
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Period (algebraic geometry) - Wikipedia
In mathematics, specifically algebraic geometry, a period or algebraic period is a complex number that can be expressed as an integral of an algebraic function over an algebraic domain. The periods are a class of numbers which includes, alongside the algebraic numbers, many well known mathematical constants … See more
The periods are intended to bridge the gap between the well-behaved algebraic numbers, which form a class too narrow to include many common mathematical constants and the See more
Many of the constants known to be periods are also given by integrals of transcendental functions. Kontsevich and Zagier note that there "seems to be no universal rule explaining why certain infinite sums or integrals of transcendental functions are periods". See more
The ring of periods can be widened to the ring of extended periods $${\displaystyle {\hat {\mathcal {P}}}}$$ by adjoining the element 1/π.
Permitting the integrand See moreWikipedia text under CC-BY-SA license Period mapping - Wikipedia
In mathematics, in the field of algebraic geometry, the period mapping relates families of Kähler manifolds to families of Hodge structures.
Wikipedia · Text under CC-BY-SA license- Estimated Reading Time: 8 mins
Algebraic geometry - Wikipedia
Algebraic geometry is a branch of mathematics which uses abstract algebraic techniques, mainly from commutative algebra, to solve geometrical problems. Classically, it studies zeros of multivariate polynomials; the modern approach …
Amplitude, Period, Phase Shift and Frequency - Math …
The Period goes from one peak to the next (or from any point to the next matching point): The Amplitude is the height from the center line to the peak (or to the trough). Or we can measure the height from highest to lowest points and …
Algebraic Period -- from Wolfram MathWorld
In algebra, a period is a number that can be written an integral of an algebraic function over an algebraic domain. More specifically, a period is a real number r=int_(P(x_1,...,x_n)>=0)Q(x_1,...,x_n)dx_1...dx_n where P is a polynomial and …
of periods generalizes in algebraic geometry and yields the theory of periods and period domains for algebraic varieties; see [2]. Kontsevich and Zagier define periods as those complex …
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Period mapping - Encyclopedia of Mathematics
Dec 20, 2019 · The study of period mappings dates back to the studies of N.H. Abel and C.G.J. Jacobi on integrals of algebraic functions (see Abelian differential). However, until recently, the …
We start with the definitions of Jacobians of curves, Prym varieties, and intermediate Jacobians, then move on to Griffiths’ construction of period domains and period maps.
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Periods - IHES
Definition 1 A period is the value of an absolutely convergent multi-variable inte-gral of a rational function with algebraic coefficients, over a domain in Rn given by polynomial inequalities with …
algebraic geometry - Definition of a period using cohomology ...
Definition of a period using cohomology. In algebraic geometry, a period is an integral of an algebraic function over an algebraic domain (for instance, 2iπ = ∫∂D(0,1) dz z 2 i π = ∫ ∂ D (0, 1) …
Periods in algebraic geometry and number theory
Feb 18, 2022 · Roughly speaking, periods are numbers that arise as integrals of polynomial differential forms over sets that are cut out by polynomial equations. More conceptually, …
algebraic geometry - What does the Grothendieck's period …
I would like to know how is the Grothendieck's period conjecture about algebraic cycles, defined explicitly ? and, what link has it with the Hodge conjecture for smooth complexe algebraic …
Geometry - Wikipedia
Geometry (from Ancient Greek γεωμετρία (geōmetría) 'land measurement'; from γῆ (gê) 'earth, land' and μέτρον (métron) 'a measure') [1] is a branch of mathematics concerned with …
We explain Kont-sevich’s formal period algebra ̃P in terms of explicit generators and relations. The period conjecture simply asserts that the obvious surjective map ̃P → P is also injective. We …
Period (algebraic geometry) - atozwiki.com
In algebraic geometry a period is a number that can be expressed as an integral of an algebraic function over an algebraic domain. Sums and products
Period (algebraic geometry) - Wikiwand
In mathematics, specifically algebraic geometry, a period or algebraic period[1] is a complex number that can be expressed as an integral of an algebraic function over an algebraic …
algebraic geometry - Why does Grothendieck's period conjecture …
May 19, 2013 · Can you explain to me why the Grothendieck period conjecture implies the Hodge conjecture only for abelian varieties, but not for non-singular complex algebraic varieties for …
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PERIODS - IHES
Algebra: An y p olynomial equation a 0 + 1 x n n 1 = 0; n > with complex co e cien ts has a solution x 2 C. In particular, w e can consider the set of all x 2 C suc h that satis es an …
Talk:Period (algebraic geometry) - Wikipedia
Proving that volume of a given semialgebraic set (which is what the definition of a period actually calls for, it's not really an integral) can be approximated to an arbitrary given accuracy by an …
ag.algebraic geometry - What are reasons to believe that e is not …
Periods arise from the comparison between Betti and de Rham cohomology for an algebraic variety. The Period Conjecture, due to Grothendieck, is a transcendence conjecture for …
Period (algebraic geometry) - Detailed Pedia
In algebraic geometry, a period is a number that can be expressed as an integral of an algebraic function over an algebraic domain. Sums and products of periods remain periods, such that …
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