Italian school of algebraic geometry - Italian school of algebraic geometry In relation with the history of mathematics, the Italian school of algebraic geometry refers to the work over half a century or more (flourishing roughly 1885-1935) done internationally in birational geometry, particularly on algebraic surfaces. There were in the region of 30 to 40 leading mathematicians who made major contributions; about half of those being in fact Italian. There is no question that the leadership fell to the group in Rome of Guido Castelnuovo, Federigo Enriques and Francesco Severi; who were involved in some of the deepest discoveries, as well as setting the style. The fashion and foundational attitude changed in algebraic geometry from 1950 onwards, leading to an axiomatisation and some acrimony as to the status of some results. For.
List of algebraic geometry topics - List of algebraic geometry topics This is a list of algebraic geometry topics, by Wikipedia page. Table of contents showTocToggle("show","hide") 1 Classical topics 2 Foundations 3 The geometers Classical topics Affine space Projective space Projective plane Algebraic curve Elliptic curve Elliptic function Elliptic integral Hyperelliptic curve Klein quartic Bézout's theorem Genus (mathematics) Riemann surface Riemann-Roch theorem Algebraic variety Quadric Dimension of an algebraic variety Hilbert's Nullstellensatz Elimination theory Serre duality Tangent space Function field Birational geometry Algebraic group Abelian variety Grassmannian Flag manifold Algebraic torus Weil restriction Intersection number Modular form Moduli space Invariant theory Algebraic form Kähler manifold Calabi-Yau manifold Weil conjectures Hodge conjecture Foundations Commutative algebra Prime ideal Valuation (mathematics) Spectrum of a ring Affine scheme Scheme Zariski topology Sheaf Locally ringed space Grothendieck topology.
Birational geometry - Birational geometry In mathematics, birational geometry is a part of the subject of algebraic geometry, that deals with the geometry of an algebraic variety that is dependent only on its function field. In the case of dimension 2, the birational geometry of algebraic surfaces was largely worked out by the Italian school of algebraic geometry, two decades on either side of the year 1900. From about 1970 advances have been made, giving a good theory of birational geometry for dimension 3. Birational geometry is largely a geometry of transformations; but it doesn't fit exactly with the Erlangen programme. One reason is that its nature is to deal with transformations that are only defined on an open, dense subset of an algebraic varieties. Such transformations, given by rational.
Projective geometry - Projective geometry In a historical perspective on mathematics, the field of geometry that developed in the first half of the nineteenth century under the name projective geometry was a stepping stone from analytic geometry to algebraic geometry. When treated in terms of homogeneous co-ordinates it looks like an extension or technical improvement of the use of co-ordinates to reduce geometric problems to algebra, that reduced the number of special cases. And on the other hand the detailed study of quadrics and the 'line geometry' of Julius Plucker still forms a rich set of examples for geometers who also work with more general concepts. Towards the end of the century the Italian school (Enriques, Segre, Severi) broke out of the traditional subject matter into an area demanding deeper.
Joseph Louis Lagrange - 25, 1736 - April 10, 1813 was an Italian mathematician/astronomer; who later lived in France and Prussia. Lagrange worked for Frederick II, in Berlin, for twenty years. It was Lagrange who developed the Mean Value Theorem and solved the isoperimetrical problem. Table of contents showTocToggle("show","hide") 1 Early years 2 Middle years 3 Later years 4 References 5 See Also Early years He was born in Turin. His father, who had charge of the Sardinian military chest, was of good social position and wealthy, but before his son grew up he had lost most of his property in speculations, and young Lagrange had to rely for his position on his own abilities. He was educated at the college of Turin, but it was not until he was seventeen that he showed any.
John Arthur Todd - Cambridge for the rest of his working life. The Todd class in the theory of the higher-dimensional Riemann-Roch theorem is an example of a characteristic class (or, more accurately, a reciprocal of one) that was discovered by Todd in work published in 1937. It used the methods of the Italian school of algebraic geometry. The Todd-Coxeter process for coset enumeration is a major method of computational algebra, and dates from a collaboration with H.S.M. Coxeter in 1936..
Galileo Galilei - (February 15, 1564 - January 8, 1642), was an Italian astronomer, philosopher, and physicist who is commonly associated with the Scientific Revolution. He has been referred to as the "father of modern astronomy" (a title to which Kepler has perhaps a stronger claim), as the "father of modern physics", and as "father of science". Along with Bacon, he pioneered the modern scientific method. Galileo was born in Pisa and his career coincided with that of Kepler. The work of Galileo is considered to be a significant break from that of Aristotle; in particular, Galileo placed emphasis on quantity, rather than quality. Table of contents showTocToggle("show","hide") 1 Experimental science 2 Astronomy 3 Physics 4 Mathematics 5 Technology 6 Church controversy 7 Quotes 8 Writings by Galileo 9 References 10 Other sources Experimental.
Characteristic class - mathematics, the idea of characteristic class is one of the unifying geometry concepts in algebraic topology, differential geometry and algebraic geometry. The theory explains, in very general terms, why fiber bundles cannot always have sections. Chararcteristic classes are in an essential way phenomena of cohomology theory - they are contravariant constructions, in the way that a section is a kind of function on a space, and to lead to a contradiction from the existence of a section we do need that variance. In fact cohomology theory grew up after homology and homotopy theory, which are both covariant theories based on mapping into a space; and characteristic class theory in its infancy in the 1930s (as part of obstruction theory) was one major reason why a 'dual' theory to homology was sought..
W. V. D. Hodge - 1975) was a Scottish mathematician, specifically a geometer. His discovery of topological relations between algebraic geometry and differential geometry - now called Hodge theory and pertaining more generally to Kähler manifolds - was a major influence on subsequent work. He was born in Edinburgh, and was a professor at Cambridge from 1936 to 1970. Amongst other honours, he received the Copley Medal of the Royal Society The Hodge index theorem was a result on the intersection number theory for curves on an algebraic surface: it determines the signature of the corresponding quadratic form. This result was sought by the Italian school of algebraic geometry, but was proved by the topological methods of Lefschetz. The Theory and Applications of Harmonic Integrals summed up Hodge's development during the 1930s of his general theory..
Scheme (mathematics) - mathematics, a scheme is an important concept connecting the fields of algebraic geometry, commutative algebra and number theory. Schemes were introduced by Alexander Grothendieck so as to broaden the notion of algebraic variety; some consider schemes to be the basic object of study of modern algebraic geometry. Technically, a scheme is a topological space together with commutative rings for all its open sets, which arises from "gluing together" spectra (spaces of prime ideals) of commutative rings. Table of contents showTocToggle("show","hide") 1 History and motivation 2 Definitions 3 The category of schemes 4 Types of schemes 5 OX modules History and motivation The algebraic geometers of the Italian school had often used the somewhat foggy concept of "generic point" when proving statements about algebraic varieties. What is true for the generic point.
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 the complex analysis of a connected compact Riemann surface with the surface's purely topological genus g, in a way that can be carried over into purely algebraic settings. Initially proved as Riemann's inequality, the theorem reached its definitive form for Riemann surfaces after work of Riemann's student Roch in the 1850s. It was later generalized to algebraic curves, to higher-dimensional varieties and beyond. Table of contents showTocToggle("show","hide") 1 Some data 2 Statement of the theorem 3 A long road of generalisation Some data We start with a connected compact Riemann surface of genus g, and.
Oscar Zariski - one of the most influential mathematicians working in the filed of algebraic geometry in the twentieth century. He was born as Ascher Zaritsky on 24 April 1899, in Kobrin (now in Belarus, then in Russia) in a Jewish family. He was a student at the University of Kiev in 1918, moving to Rome to study in 1920. He became a disciple of the Italian school of algebraic geometry, studying with Guido Castelnuovo, Federigo Enriques and Francesco Severi. He wrote a doctoral dissertation in 1924, on a topic in Galois theory. It was when it came to be published that he accepted a suggestion to change his name for professional purposes. He emigrated to the USA in 1927, supported by Solomon Lefschetz. He had a position at Johns Hopkins University, where he.
List of mathematical topics (G-I) - Generalized permutation matrix -- Generalized Riemann hypothesis -- Generalized special orthogonal group -- Generalized Woodall number -- Generalized Woodall prime -- Generating function -- Generating set -- Generating set of a group -- Generating trigonometric tables -- Genetic algorithm -- Gentzen, Gerhard -- Germ (mathematics) -- Genus -- Geodesic -- Geodesic dome -- Geodesic flow -- Geographic coordinate system -- Geometer -- Geometers -- Geometric algebra -- Geometric Brownian motion -- Geometric distribution -- Geometric isomerism -- Geometric kite -- Geometric mean -- Geometric primitive -- Geometric progression -- Geometric series -- Geometric shape -- Geometric solid -- Geometry -- Geometry of numbers -- Gergonne point -- Germain -- Germain, Sophie -- Gibbard-Satterthwaite theorem -- Gibbs-Helmholtz equation -- Gibbs' phase rule -- Gibbs phenomenon -- Gift wrapping algorithm -- Gimel function.
Algebraic geometry - Algebraic geometry Algebraic geometry is a branch of mathematics which, as the name suggests, combines abstract algebra, especially commutative algebra, with geometry. It can be seen as the study of solution sets of systems of algebraic equations. Table of contents showTocToggle("show","hide") 1 Zeroes of simultaneous polynomials 2 Affine varieties 3 Coordinate ring of a variety 4 Projective theory 5 Background to the current point of view on the subject Zeroes of simultaneous polynomials In algebraic geometry, the geometric objects studied are defined as the set of zeroes of a number of polynomials: meaning the set of common zeroes, or equally the set defined by one or several simultaneous polynomial equations. For instance, the two-dimensional sphere in three-dimensional Euclidean space R3 could be defined as the set.
James Clerk Maxwell - contributions to the fundamental models of nature. In 1931, on the centennial anniversary of Maxwell's birth, Einstein described Maxwell's work as the "most profound and the most fruitful that physics has experienced since the time of Newton." Algebraic mathematics with elements of geometry are a feature of much of Maxwell's work. Maxwell demonstrated that electric and magnetic forces are two complementary aspects of electromagnetism. He showed that electric and magnetic fields travel through space, in the form of waves, at a constant velocity of 3.0 × 108 m/s. He also proposed that light was a form of electromagnetic radiation. The scientific compound derived CGS unit measuring magnetic flux (commonly abbreviated as f ), the maxwell (Mx), was named in his honor. There is a mountain range on Venus, Maxwell Montes, named.
Jean-Pierre Serre - the leading mathematicians of the twentieth century, active in algebraic geometry, number theory and topology. Serre was awarded the Fields Medal in 1954, and was the first recipient of the Abel Prize in 2003. He was educated at the Lycée de Nimes and then from 1945 to 1948 at the Ecole Normale Supérieure in Paris. Serre was awarded his doctorate from the Sorbonne in 1951. From 1948 to 1954 he held positions at the Centre National de la Recherche Scientifique in Paris. He is a member of the French Academy of Science. From very young he was an outstanding figure in the school of Henri Cartan, working on algebraic topology, several complex variables and then commutative algebra and algebraic geometry; in a context of sheaf theory and homological algebra techniques. In.
Josip Plemelj - a year old. His mother Marija, née Mrak, found bringing up the family alone very hard, but she was able to send her son to school in Ljubljana where Plemelj studied from 1886 to 1894. After leaving and obtaining the necessary examination results he went to Vienna in 1894 where he had applied to Faculty of Arts to study mathematics, physics and astronomy. His professors in Vienna were Gustav Ritter von Escherich for mathematical analysis, Leopold Bernhard Gegenbauer and Franz Mertens for Arithmetic and Algebra, Edmund Weiss for astronomy, Jožef Stefan's student Ludwig Boltzmann for physics. On May 1898 Plemelj presented his doctoral thesis under Escherich's tutelage entitled O linearnih homogenih diferencialnih enačbah z enolično periodičnimi koeficienti (Über lineare homogene Differentialgleichungen mit eindeutigen periodischen Koeffizienten, About linear homogeneous differential equations with.
John Wallis - is also credited with introducing the infinity symbol, ∞. John Wallis was born at Ashford, Kent. He was educated at Felstead school, and at the age of fifteen mastered arithmetic after becoming fascinated by his brother's book on the topic. As it was intended that he should be a doctor, he was sent to Emmanuel College, Cambridge, while there he kept an act on the doctrine of the circulation of the blood; that was said to have been the first occasion in Europe on which this theory was publicly maintained in a disputation. His interests, however, centred on mathematics. He was elected to a fellowship at Queens' College, Cambridge, and subsequently took orders, but on the whole adhered to the Puritan party, to whom he rendered great assistance in deciphering the.
Isaac Newton (in-depth biography) - property, died before his son's birth, a few months after his marriage to Hannah Ayscough, a daughter of James Ayscough of Market-Overton. When Newton was two years old his mother married Barnabas Smith, rector of North Witham. Of this marriage there was issue, Benjamin, Mary and Hannah Smith, and to their children Sir Isaac Newton subsequently left most of his property. After a rudimentary education at two small schools in hamlets close to Woolsthorpe, Newton was sent at the age of twelve to the grammar school of Grantham. While attending Grantham school Newton lived in the house of Mr Clark, an apothecary. According to his own confession he was far from industrious, and did poorly in his class. An unprovoked attack from the boy next above him led to a fight,.
Gaspard Monge - — 1818), was a French mathematician and inventor of descriptive geometry. He was born at Beaune on the May 10 1746. He was educated first at the college of the Oratorians at Beaune, and then in their college at Lyons--where, at sixteen, the year after he had been learning physics, he was made a teacher of it. Returning to Beaune for a vacation, he made, on a large scale, a plan of the town, inventing the methods of observation and constructing the necessary instruments; the plan was presented to the town, and preserved in their library. An officer of engineers seeing it wrote to recommend Monge to the commandant of the military school at Mézières, and he was received as a draftsman and pupil in the practical school attached to that.
