In algebraic geometry and the theory of complex manifolds, a logarithmic differential form is a differential form with poles of a certain kind. The concept was introduced by Pierre Deligne.[1] In short, logarithmic differentials have the mildest possible singularities needed in order to give information about an open submanifold (the complement of the divisor of poles). (This idea is made precise by several versions of de Rham's theorem discussed below.)
Let X be a complex manifold, D ⊂ X a reduced divisor (a sum of distinct codimension-1 complex subspaces), and ω a holomorphic p-form on X−D. If both ω and dω have a pole of order at most 1 along D, then ω is said to have a logarithmic pole along D. ω is also known as a logarithmic p-form. The p-forms with log poles along D form a subsheaf of the meromorphic p-forms on X, denoted
The name comes from the fact that in complex analysis, ; here is a typical example of a 1-form on the complex numbers C with a logarithmic pole at the origin. Differential forms such as make sense in a purely algebraic context, where there is no analog of the logarithm function.
geometry and the theory of complex manifolds, a logarithmic differential form is a differential form with poles of a certain kind. The concept was introduced...
A logarithmic spiral, equiangular spiral, or growth spiral is a self-similar spiral curve that often appears in nature. The first to describe a logarithmic...
In mathematics, specifically in calculus and complex analysis, the logarithmic derivative of a function f is defined by the formula f ′ f {\displaystyle...
differentiation Logarithmic distribution LogarithmicformLogarithmic graph paper Logarithmic growth Logarithmic identities Logarithmic number system Logarithmic scale...
the log semiring. Logarithmic one-forms df/f appear in complex analysis and algebraic geometry as differential forms with logarithmic poles. The polylogarithm...
canonical divisor of X. A logarithmic 1-form on a log pair (X,D) is allowed to have logarithmic singularities of the form d log(z) = dz/z along components...
{\displaystyle K_{\text{a}}=\mathrm {\frac {[A^{-}][H^{+}]}{[HA]}} ,} or by its logarithmicform p K a = − log 10 K a = log 10 [ HA ] [ A − ] [ H + ] {\displaystyle...
{\gamma }}^{n}} The Ostwald and de Waele equation can be written in a logarithmicform: log ( τ ) = log ( K ) + n log ( γ ˙ ) {\displaystyle \log(\tau...
signum logarithmic function shown above. All of these antiderivatives can be derived using integration by parts and the simple derivative forms shown above...
A logarithmic timeline is a timeline laid out according to a logarithmic scale. This necessarily implies a zero point and an infinity point, neither of...
\gamma \approx 0.577} is the Euler–Mascheroni constant. The leading, logarithmic term is frequently used, and resembles the Coulomb logarithm that occurs...
functions like the logarithmic sine, logarithmic cosine, logarithmic secant, logarithmic cosecant, logarithmic tangent and logarithmic cotangent. The word...
In geometry, a golden spiral is a logarithmic spiral whose growth factor is φ, the golden ratio. That is, a golden spiral gets wider (or further from...
calculus, logarithmic differentiation or differentiation by taking logarithms is a method used to differentiate functions by employing the logarithmic derivative...
arithmetic to the geometric composition of angles. Marking the line with logarithmically spaced graduations associates multiplication and division with geometric...
to study semistable schemes, and in particular the notion of logarithmic differential form and the related Hodge-theoretic concepts. This idea has applications...
potentiometer has a resistance, taper, or, "curve" (or law) of a logarithmic (log) form, is used as the volume control in audio power amplifiers, where...
substituted into the link budget equation above, the result is the logarithmicform of the Friis transmission equation. In some cases, it is convenient...
form or, more commonly, in polar form. The S-parameter magnitude may be expressed in linear form or logarithmicform. When expressed in logarithmic form...
In mathematics, many logarithmic identities exist. The following is a compilation of the notable of these, many of which are used for computational purposes...
conditions lead to the Bethe ansatz equations or simply Bethe equations. In logarithmicform the Bethe ansatz equations can be generated by the Yang action. The...
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