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See all on WikipediaPeriod (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 …
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 …
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 …
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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) …
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
About: Period (algebraic geometry) - DBpedia Association
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, so 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.
Different occurences of the word 'period' in algebraic geometry
Dec 23, 2021 · (2) Period: A real number is a period if it is an integral ∫p≥0 q(x1, …,xn)dx ∫ p ≥ 0 q (x 1, …, x n) d x where p p is a polynomial with rational coefficients and q q is a rational …
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 …
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 …
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, …
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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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 …
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 …
Period (algebraic geometry) – Wikipedia – Enzyklopädie - Opalstack
Jan 8, 2018 · 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, …
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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 …
Algebra - Wikipedia
Algebra is the branch of mathematics that studies algebraic structures and the operations they use. [1] An algebraic structure is a non-empty set of mathematical objects, such as the …
period in nLab - ncatlab.org
Sep 15, 2024 · Periods appear in a number of situations in classical algebraic geometry. Specific matrices of periods are defined and important in the theory of algebraic functions, Hodge …
Algebraische Periode – Wikipedia
Die Klasse der algebraischen Perioden als eine Teilmenge der komplexen Zahlen. In der Mathematik, insbesondere in der algebraischen Geometrie, ist eine algebraische Periode [1] …
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