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Max Noether's Theorem
In algebraic geometry, Max Noether's theorem may refer to the results of Max Noether: * Several closely related results of Max Noether on canonical curves * AF+BG theorem, or Max Noether's fundamental theorem, a result on algebraic curves in the projective plane, on the residual sets of intersections * Max Noether's theorem on curves lying on algebraic surfaces, which are hypersurfaces in ''P''3, or more generally complete intersections * Noether's theorem on rationality for surfaces * Max Noether theorem on the generation of the Cremona group by quadratic transformations See also *Noether's theorem, usually referring to a result derived from work of Max's daughter Emmy Noether *Noether inequality * Special divisor *Hirzebruch–Riemann–Roch theorem In mathematics, the Hirzebruch–Riemann–Roch theorem, named after Friedrich Hirzebruch, Bernhard Riemann, and Gustav Roch, is Hirzebruch's 1954 result generalizing the classical Riemann–Roch theorem on Riemann surfaces t ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Max Noether
Max Noether (24 September 1844 – 13 December 1921) was a German mathematician who worked on algebraic geometry and the theory of algebraic functions. He has been called "one of the finest mathematicians of the nineteenth century". He was the father of Emmy Noether. Biography Max Noether was born in Mannheim in 1844, to a Jewish family of wealthy wholesale hardware dealers. His grandfather, Elias Samuel, had started the business in Bruchsal in 1797. In 1809 the Grand Duchy of Baden established a "Tolerance Edict", which assigned a hereditary surname to the male head of every Jewish family which did not already possess one. Thus the Samuels became the Noether family, and as part of this Christianization of names, their son Hertz (Max's father) became Hermann. Max was the third of five children Hermann had with his wife Amalia Würzburger. At 14, Max contracted polio and was afflicted by its effects for the rest of his life. Through self-study, he learned advanced mathematics ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Canonical Curve
In mathematics, the canonical bundle of a non-singular algebraic variety V of dimension n over a field is the line bundle \,\!\Omega^n = \omega, which is the nth exterior power of the cotangent bundle \Omega on V. Over the complex numbers, it is the determinant bundle of the holomorphic cotangent bundle T^*V. Equivalently, it is the line bundle of holomorphic n-forms on V. This is the dualising object for Serre duality on V. It may equally well be considered as an invertible sheaf. The canonical class is the divisor class of a Cartier divisor K on V giving rise to the canonical bundle — it is an equivalence class for linear equivalence on V, and any divisor in it may be called a canonical divisor. An anticanonical divisor is any divisor −K with K canonical. The anticanonical bundle is the corresponding inverse bundle \omega^. When the anticanonical bundle of V is ample, V is called a Fano variety. The adjunction formula Suppose that X is a smooth variety and ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
AF+BG Theorem
AF, af, Af, etc. may refer to: Arts and entertainment *A-F Records, Pittsburgh, Pennsylvania *''Almost Family'', US TV series Businesses and organizations European * ÅF, a Swedish technical consulting company * AF Gruppen, a construction company, Norway * Action Française, a French political movement * Air France, IATA code and stock symbol * Anarchist Federation (British Isles) International * Abercrombie & Fitch, A&F, US clothing shops * The Adaptation Fund, for climate change adaptation, UN * Adventist Forums, of Seventh-day Adventists Elsewhere * American Freightways, US trucking company, merged into FedEx Freight Language * Académie française, for French language matters * Alliance Française, promoting French language and culture * Acronym Finder, an online database * Afrikaans language (ISO 639-1 language code AF) * "...as fuck", meaning "very", in SMS language Medicine * Amniotic fluid * Atrial fibrillation, an abnormal heart rhythm Military * AF Guardian, a US Nav ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Max Noether's Theorem On Curves
In algebraic geometry, Max Noether's theorem on curves is a theorem about curves lying on algebraic surfaces, which are hypersurfaces in ''P''3, or more generally complete intersections. It states that, for degree at least four for hypersurfaces, the '' generic'' such surface has no curve on it apart from the hyperplane section. In more modern language, the Picard group is infinite cyclic In abstract algebra, a cyclic group or monogenous group is a Group (mathematics), group, denoted C_n (also frequently \Z_n or Z_n, not to be confused with the commutative ring of P-adic number, -adic numbers), that is Generating set of a group, ge ..., other than for a short list of degrees. This is now often called the Noether-Lefschetz theorem. {{algebraic-geometry-stub Algebraic geometry ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Noether's Theorem On Rationality For Surfaces
In mathematics, Noether's theorem on rationality for surfaces is a classical result of Max Noether on complex algebraic surfaces, giving a criterion for a rational surface. Let ''S'' be an algebraic surface that is non-singular and projective. Suppose there is a morphism φ from ''S'' to the projective line, with ''general fibre'' also a projective line. Then the theorem states that ''S'' is rational. See also * Hirzebruch surface *List of complex and algebraic surfaces This is a list of named algebraic surfaces, compact complex surfaces, and families thereof, sorted according to their Kodaira dimension following Enriques–Kodaira classification. Kodaira dimension −∞ Rational surfaces * Projective plane Qu ... ReferencesCastelnuovo’s Theorem Notes Algebraic surfaces Theorems in algebraic geometry {{algebraic-geometry-stub ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Cremona Group
In birational geometry, the Cremona group, named after Luigi Cremona, is Birational geometry#Birational automorphism groups, the group of birational automorphisms of the n-dimensional projective space over a Field (mathematics), field , also known as Cremona transformations. It is denoted by Cr(\mathbb^n(k)), Bir(\mathbb^n(k)) or Cr_n(k). Historical origins The Cremona group was introduced by the italian mathematician . However, some historians consider Isaac Newton as a "founder of the theory of Cremona transformations" through his work done two centuries before, in 1667 and 1687. Contributions were also made by Hilda Phoebe Hudson in the 1900s. Basic properties The Cremona group is naturally identified with the automorphism group \mathrm_k(k(x_1, ..., x_n)) of the rational function, field of the rational functions in n Indeterminate (variable), indeterminates over k. Here, the field k(x_1, ..., x_n) is a pure transcendental extension of k, with transcendence degree n. The p ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Noether's Theorem
Noether's theorem states that every continuous symmetry of the action of a physical system with conservative forces has a corresponding conservation law. This is the first of two theorems (see Noether's second theorem) published by the mathematician Emmy Noether in 1918. The action of a physical system is the integral over time of a Lagrangian function, from which the system's behavior can be determined by the principle of least action. This theorem applies to continuous and smooth symmetries of physical space. Noether's formulation is quite general and has been applied across classical mechanics, high energy physics, and recently statistical mechanics. Noether's theorem is used in theoretical physics and the calculus of variations. It reveals the fundamental relation between the symmetries of a physical system and the conservation laws. It also made modern theoretical physicists much more focused on symmetries of physical systems. A generalization of the formulations ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Noether Inequality
In mathematics, the Noether inequality, named after Max Noether, is a property of compact minimal complex surfaces that restricts the topological type of the underlying topological 4-manifold. It holds more generally for minimal projective surfaces of general type over an algebraically closed field. Formulation of the inequality Let ''X'' be a smooth minimal projective surface of general type defined over an algebraically closed field (or a smooth minimal compact complex surface of general type) with canonical divisor ''K'' = −''c''1(''X''), and let ''p''g = ''h''0(''K'') be the dimension of the space of holomorphic two forms, then : p_g \le \frac c_1(X)^2 + 2. For complex surfaces, an alternative formulation expresses this inequality in terms of topological invariants of the underlying real oriented four manifold. Since a surface of general type is a Kähler surface, the dimension of the maximal positive subspace in intersection form on the second cohomology is given by ' ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Special Divisor
Special or specials may refer to: Policing * Specials, Ulster Special Constabulary, the Northern Ireland police force * Specials, Special Constable, an auxiliary, volunteer, or temporary; police worker or police officer * Special police forces Military * Special forces * Special operations Literature * ''Specials'' (novel), a novel by Scott Westerfeld * ''Specials'', the comic book heroes, see ''Rising Stars'' (comic) Film and television * Special (lighting), a stage light that is used for a single, specific purpose * ''Special'' (film), a 2006 scifi dramedy * ''The Specials'' (2000 film), a comedy film about a group of superheroes * Special 26, a 2013 Indian Hindi-language period heist thriller film * ''The Specials'' (2019 film), a film by Olivier Nakache and Éric Toledano * Television special, television programming that temporarily replaces scheduled programming * ''Special'' (TV series), a 2019 Netflix Original TV series * ''Specials'' (TV series), a 1991 TV series ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
