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The rational numbers (), algebraic numbers (), algebraic periods and exponential periods as subsets of the complex numbers ().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 domain.
The period matrix of X 0 with respect to these bases is the matrix ... Voisin, Hodge Theory and Complex Algebraic Geometry I, II; Applications
In the same period began the algebraization of the algebraic geometry through commutative algebra. The prominent results in this direction are Hilbert's basis theorem and Hilbert's Nullstellensatz , which are the basis of the connection between algebraic geometry and commutative algebra, and Macaulay 's multivariate resultant , which is the ...
For applications in algebraic geometry, namely, classification of complex projective varieties by their periods, the set of all Hodge structures of weight on is too big. Using the Riemann bilinear relations , in this case called Hodge Riemann bilinear relations , it can be substantially simplified.
In mathematics, more specifically in algebraic geometry, the Griffiths group of a projective complex manifold X measures the difference between homological equivalence and algebraic equivalence, which are two important equivalence relations of algebraic cycles. More precisely, it is defined as
Period matrix – period matrices are a useful technique for computing the Jacobian of a curve; ... Hartshorne, Robin (19 December 1977), Algebraic Geometry, ...
This formalism (and the name period ring) grew out of a few results and conjectures regarding comparison isomorphisms in arithmetic and complex geometry: If X is a proper smooth scheme over C, there is a classical comparison isomorphism between the algebraic de Rham cohomology of X over C and the singular cohomology of X(C)
Period (algebraic geometry), numbers that can be expressed as integrals of algebraic differential forms over algebraically defined domains, forming a ring Science Period (gene) , a gene in Drosophila involved in regulating circadian rhythm