meromorphic curve
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Meromorphic function — In complex analysis, a meromorphic function on an open subset D of the complex plane is a function that is holomorphic on all D except a set of isolated points, which are poles for the function. (The terminology comes from the Ancient Greek meros … Wikipedia
Modular curve — In number theory and algebraic geometry, a modular curve Y(Γ) is a Riemann surface, or the corresponding algebraic curve, constructed as a quotient of the complex upper half plane H by the action of a congruence subgroup Γ of the modular group of … Wikipedia
Riemann surface — For the Riemann surface of a subring of a field, see Zariski–Riemann space. Riemann surface for the function ƒ(z) = √z. The two horizontal axes represent the real and imaginary parts of z, while the vertical axis represents the real… … Wikipedia
Riemann–Roch theorem — In mathematics, specifically in complex analysis and algebraic geometry, the Riemann–Roch theorem is an important tool in the computation of the dimension of the space of meromorphic functions with prescribed zeroes and allowed poles. It relates… … Wikipedia
Complex plane — Geometric representation of z and its conjugate in the complex plane. The distance along the light blue line from the origin to the point z is the modulus or absolute value of z. The angle φ is the argument of z. In mathematics … Wikipedia
Partial fractions in complex analysis — In complex analysis, a partial fraction expansion is a way of writing a meromorphic function f(z) as an infinite sum of rational functions and polynomials. When f(z) is a rational function, this reduces to the usual method of partial… … Wikipedia
Gamma function — For the gamma function of ordinals, see Veblen function. The gamma function along part of the real axis In mathematics, the gamma function (represented by the capital Greek letter Γ) is an extension of the factorial function, with its… … Wikipedia
Modular form — In mathematics, a modular form is a (complex) analytic function on the upper half plane satisfying a certain kind of functional equation and growth condition. The theory of modular forms therefore belongs to complex analysis but the main… … Wikipedia
Divisor (algebraic geometry) — In algebraic geometry, divisors are a generalization of codimension one subvarieties of algebraic varieties; two different generalizations are in common use, Cartier divisors and Weil divisors (named for Pierre Cartier and André Weil). These… … Wikipedia
Enriques-Kodaira classification — In mathematics, the Enriques Kodaira classification is a classification of compact complex surfaces. For complex projective surfaces it was done by Federigo Enriques, and Kunihiko Kodaira later extended it to non algebraic compact surfaces. It… … Wikipedia
Weierstrass's elliptic functions — In mathematics, Weierstrass s elliptic functions are elliptic functions that take a particularly simple form; they are named for Karl Weierstrass. This class of functions are also referred to as p functions and generally written using the symbol… … Wikipedia
