Eksempler på brug af Algebraic surfaces på Engelsk og deres oversættelser til Dansk
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During this period Zariski wrote Algebraic Surfaces which was published in 1935.
I denne periode Zariski skrev Algebraisk Flader, der blev offentliggjort i 1935.Besides this he has made several important contributions to the theory of algebraic surfaces.
Ud over dette har han gjort adskillige vigtige bidrag til teorien om algebraiske overflader.In 1890 Castelnuovo studied and classified algebraic surfaces with hyperelliptic prime sections.
I 1890 Castelnuovo undersøgt og klassificeret algebraisk overflader med hyperelliptiske prime sektioner.During the years in which she was writing her major treatise Hudson returned to publishing on Cremona transformations and algebraic surfaces.
I løbet af de år, hvor hun skriver hendes store afhandling Hudson returneres til udgivelse på Cremona omdannelser og algebraisk overflader.He took Castelnuovo 's advice and worked on algebraic surfaces, sometimes collaborating with Castelnuovo.
Han tog Castelnuovo's rådgivning og arbejdede på algebraiske flader, undertiden samarbejder med Castelnuovo.He worked on algebraic surfaces, especially during his time in Rome, and later in his career du Val became interested in elliptic functions.
Han arbejdede på algebraisk overflader, især under hans tid i Rom, og senere i hans karriere du Val blev interesseret i elliptiske funktioner.Enriques struggled with the concepts as he tried to understand the theory of algebraic surfaces, making mistakes in his attempts.
Enriques kæmpede med begreber som han forsøgte at forstå teorien om algebraiske flader, laver fejl i sit forsøg.Their classification of algebraic surfaces was published in 1914 but their collaboration had led to many joint papers during the course of the work.
Deres klassificering af algebraisk overflader blev offentliggjort i 1914, men deres samarbejde havde ført til mange fælles papirer i løbet af arbejdet.On the whole,the book contains a very large mass of information about algebraic surfaces over the field of complex numbers.
I det store oghele bogen indeholder en meget stor masse af information om algebraisk overflader over marken af komplekse numre.Castelnuovo produced a series of papers over a period of 20 years which,together with Enriques, finally produced a classification of algebraic surfaces.
Castelnuovo udarbejdet en række papirer over en periode på 20 år,som sammen med Enriques endelig udarbejdet en klassificering af algebraisk overflader.Also before 1920 Alexander had made fundamental contributions to the theory of algebraic surfaces and to the study of Cremona transformations.
Også før 1920 Alexander havde gjort grundlæggende bidrag til teorien om algebraiske flader og til undersøgelse af Cremona forandringer.He began to write on mechanics and he also made significant contributions to algebraic geometry,particularly the theory of algebraic surfaces.
Han begyndte at skrive om mekanik, og han også gjort betydelige bidrag til His work on algebraic surfaces gained world-wide recognition when it was highlighted by H F Baker in his presidential address to the International Congress in Cambridge in 1912.
Hans arbejde på algebraisk overflader vundet hele verden anerkendelse, da det blev fremhævet af HF Baker i sin præsidentkandidat adresse til den internationale kongres i Cambridge i 1912.Mori took the decisive steps over a ten-year period in extending the classical theory of algebraic surfaces to dimension three.
Mori tog afgørende skridt over en ti-årig periode i forlængelse af den klassiske teori om algebraisk overflader til dimension tre.Major progress was made on classifying algebraic surfaces during the first part of the 20th century by the great Italian algebraic geometers led by Castelnuovo, Enriques and Severi.
Blev der gjort store fremskridt på klassificering algebraisk overflader i den første del af det 20 århundrede af den store italienske Mumford has carried forward, after Zariski, the project of making algebraic andrigorous the work of the Italian school on algebraic surfaces.
Mumford har fremført, efter Zariski, at projektet med at gøre Mori took the decisive steps over a ten-year period in extending the classical theory of algebraic surfaces to dimension three: prior to Mori's breakthroughs this problem seemed out of reach.
Mori tog afgørende skridt over en ti-årig periode i forlængelse af den klassiske teori om algebraisk overflader til dimension tre: før Mori's gennembrud dette problem syntes uden for rækkevidde.Having instigated the Colloquium Lectures, as we described above,he was a Colloquium Lecturer himself in 1903 when he lectured on Linear systems of curves on algebraic surfaces.
Efter at have indledt den kollokvium foredrag,som vi beskrev ovenfor, han var et kollokvium Underviser sig selv i 1903, da han underviser på en lineær systemer i kurver på algebraisk overflader.Building on work by Abel and Riemann,Picard's study of the integrals attached to algebraic surfaces and related topological questions developed into an important part of algebraic geometry.
Bygget på arbejde af Abel og Riemann,Picard's undersøgelse af integrals knyttet til algebraisk overflader og beslægtede topologiske spørgsmål udviklet sig til en vigtig del af Volume 4 considers higher dimensions, mainly dimensions four and five,while the final two volumes cover the analytical principles of the theory of curves and the theory of algebraic surfaces and higher loci.
Bind 4 mener højere dimensioner, hovedsagelig dimensioner fire og fem, mensde sidste to volumener dække de analytiske principper i den teori om kurver og teorien om algebraiske flader og højere loci.In[Algebraic Surfaces] I tried my best to present the underlying ideas of the ingenious geometric methods and proofs with which the Italian geometers were handling these deeper aspects of the whole theory of surfaces. .
I[Algebraisk Flader] Jeg prøvede mit bedste for at præsentere de underliggende ideer af geniale geometriske metoder og beviser, som den italienske geometers blev håndterer disse dybere aspekter af hele teorien om overflader.At first the collaboration was between the established mathematician Castelnuovo and the young twenty year old Enriques so the relationship was that of teacher and student.Enriques struggled with the concepts as he tried to understand the theory of algebraic surfaces, making mistakes in his attempts.
Ved første samarbejdet var mellem de etablerede matematiker Castelnuovo og de unge tyve år gamle Enriques så forholdet var lærer og elev.Enriques kæmpede med begreber som han forsøgte at forstå teorien om algebraiske flader, laver fejl i sit forsøg.In[Algebraic Surfaces] I tried my best to present the underlying ideas of the ingenious geometric methods and proofs with which the Italian geometers were handling these deeper aspects of the whole theory of surfaces… I began to feel distinctly unhappy about the rigour of the original proofs(without losing in the least my admiration for the imaginative geometric spirit that permeated these proofs); I became convinced that the whole structure must be done over again by purely algebraic methods.
I[Algebraisk Flader] Jeg prøvede mit bedste for at præsentere de underliggende ideer af geniale geometriske metoder og beviser, som den italienske geometers blev håndterer disse dybere aspekter af hele teorien om overflader… Jeg begyndte at føle sig decideret utilfreds med den stramning af det oprindelige beviser(uden at tabe i de mindst min beundring for den fantasifulde geometriske ånd, at gennemsyret disse beviser); jeg blev overbevist om, at hele strukturen skal gøres igen ved rent It was a remarkably productive period for Hudson who published her first paper in the Proceedings of the London Mathematical Society in 1911, followed by three papers in 1912, and six papers on topics such as Cremona transformations, nodal curves,pinch-points, and algebraic surfaces in 1913.
Det var en bemærkelsesværdig produktiv periode, for Hudson der offentliggøres hendes første papir i Proceedings of the London Mathematical Society i 1911, efterfulgt af tre papirer i 1912, og seks papirer om emner såsom Cremona omdannelser, projekter for knudepunktsinfra kurver,knivspids-points, og algebraisk overflader i 1913.Major progress was made on classifying algebraic surfaces during the first part of the 20th century by the great Italian algebraic geometers led by Castelnuovo, Enriques and Severi. Progress in this line continued with Zariski 's contribution during the 1950s, followed by Kodaira 's work in the following decade. Mori's work achieved a remarkable continuation of classification efforts in algebraic geometry and in many ways provides a fitting chapter in the progress of algebraic geometry through the 20th century.
Blev der gjort store fremskridt på klassificering algebraisk overflader i den første del af det 20 århundrede af den store italienske He also made many discoveries about ruled surfaces and other surfaces, including the idea of the normal singularities of an algebraic surface.
Han har også gjort mange opdagelser om regerede He examined algebraic curves on an algebraic surface F(x, y, z) 0 and developed methods which enabled him to give easy proofs of deep results due to Emile Picard and Severi.
Han undersøgte Castelnuovo is also remembered for the Kronecker-Castelnuovo theorem which states:If the sections of an irreducible algebraic surface with a doubly infinite system of planes turn out to be ruler curves, then the above surface is either ruled or the Roman surface of Steiner.
Castelnuovo er også huskes for Kroneckers-Castelnuovo sætning, hvori det hedder: Hvisdele af en irreducible algebraisk overflade med en dobbelt uendelig system med fly vise sig at være lineal kurver, så ovenstående If the sections of an irreducible algebraic surface with a doubly infinite system of planes turn out to be ruler curves, then the above surface is either ruled or the Roman surface of Steiner.
Hvis dele af en irreducible algebraisk overflade med en dobbelt uendelig system med fly vise sig at være lineal kurver, så ovenstående Clebsch must also be credited with the first birational invariant of an algebraic surface, the geometric genus that he introduced as the maximal number of double integrals of the first kind existing on it.
Clebsch skal også blive krediteret med det første birational invariant af en algebraisk overflade, den geometriske slægt, at han indførte som det maksimale antal double integrals af den første slags eksisterende på det.
