|
Ruggiero Torelli
Ruggiero Torelli (7 June 1884, in Naples – 9 September 1915) was an Italian mathematician who introduced Torelli's theorem In mathematics, the Torelli theorem, named after Ruggiero Torelli, is a classical result of algebraic geometry over the complex number field, stating that a non-singular projective algebraic curve (compact Riemann surface) ''C'' is determined by it .... Publications * * See also * Torelli group References * External links Biography {{authority control Italian mathematicians ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Naples
Naples (; it, Napoli ; nap, Napule ), from grc, Νεάπολις, Neápolis, lit=new city. is the regional capital of Campania and the third-largest city of Italy, after Rome and Milan, with a population of 909,048 within the city's administrative limits as of 2022. Its province-level municipality is the third-most populous metropolitan city in Italy with a population of 3,115,320 residents, and its metropolitan area stretches beyond the boundaries of the city wall for approximately 20 miles. Founded by Greeks in the first millennium BC, Naples is one of the oldest continuously inhabited urban areas in the world. In the eighth century BC, a colony known as Parthenope ( grc, Παρθενόπη) was established on the Pizzofalcone hill. In the sixth century BC, it was refounded as Neápolis. The city was an important part of Magna Graecia, played a major role in the merging of Greek and Roman society, and was a significant cultural centre under the Romans. Naples served a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mathematician
A mathematician is someone who uses an extensive knowledge of mathematics in their work, typically to solve mathematical problems. Mathematicians are concerned with numbers, data, quantity, structure, space, models, and change. History One of the earliest known mathematicians were Thales of Miletus (c. 624–c.546 BC); he has been hailed as the first true mathematician and the first known individual to whom a mathematical discovery has been attributed. He is credited with the first use of deductive reasoning applied to geometry, by deriving four corollaries to Thales' Theorem. The number of known mathematicians grew when Pythagoras of Samos (c. 582–c. 507 BC) established the Pythagorean School, whose doctrine it was that mathematics ruled the universe and whose motto was "All is number". It was the Pythagoreans who coined the term "mathematics", and with whom the study of mathematics for its own sake begins. The first woman mathematician recorded by history was Hypati ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Torelli's Theorem
In mathematics, the Torelli theorem, named after Ruggiero Torelli, is a classical result of algebraic geometry over the complex number field, stating that a non-singular projective algebraic curve (compact Riemann surface) ''C'' is determined by its Jacobian variety ''J''(''C''), when the latter is given in the form of a principally polarized abelian variety. In other words, the complex torus ''J''(''C''), with certain 'markings', is enough to recover ''C''. The same statement holds over any algebraically closed field. From more precise information on the constructed isomorphism of the curves it follows that if the canonically principally polarized Jacobian varieties of curves of genus \geq 2 are ''k''-isomorphic for ''k'' any perfect field, so are the curves. This result has had many important extensions. It can be recast to read that a certain natural morphism, the period mapping, from the moduli space of curves of a fixed genus (mathematics), genus, to a moduli space of abelian v ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mapping Class Group
In mathematics, in the subfield of geometric topology, the mapping class group is an important algebraic invariant of a topological space. Briefly, the mapping class group is a certain discrete group corresponding to symmetries of the space. Motivation Consider a topological space, that is, a space with some notion of closeness between points in the space. We can consider the set of homeomorphisms from the space into itself, that is, continuous maps with continuous inverses: functions which stretch and deform the space continuously without breaking or gluing the space. This set of homeomorphisms can be thought of as a space itself. It forms a group under functional composition. We can also define a topology on this new space of homeomorphisms. The open sets of this new function space will be made up of sets of functions that map compact subsets ''K'' into open subsets ''U'' as ''K'' and ''U'' range throughout our original topological space, completed with their finite intersect ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
