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birationally equivalent

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  • Algebraic curve — In algebraic geometry, an algebraic curve is an algebraic variety of dimension one. The theory of these curves in general was quite fully developed in the nineteenth century, after many particular examples had been considered, starting with… …   Wikipedia

  • Montgomery curve — In mathematics the Montgomery curve is a form of elliptic curve, different from the usual representation (Weierstrass form). It has been introduced by Peter L.Montgomery in,[1] and it has been used since 1987 for certain computations, and in… …   Wikipedia

  • Supersingular K3 surface — In algebraic geometry, a supersingular K3 surface is a particular type of K3 surface. Such an algebraic surface has its cohomology generated by algebraic cycles; in other words, since the second Betti number [In the case of a base field other… …   Wikipedia

  • Rational mapping — In mathematics, in particular the subfield of algebraic geometry, a rational map is a kind of partial function between algebraic varieties. In this article we use the convention that varieties are irreducible.DefinitionA first attemptSuppose we… …   Wikipedia

  • Enriques–Kodaira classification — In mathematics, the Enriques–Kodaira classification is a classification of compact complex surfaces into ten classes. For each of these classes, the surfaces in the class can be parametrized by a moduli space. For most of the classes the moduli… …   Wikipedia

  • Heisuke Hironaka — Infobox Scientist name = Heisuke Hironaka box width = image width =150px caption = Heisuke Hironaka birth date = April 9, 1931 birth place = death date = death place = residence = citizenship = nationality = Japan ethnicity = field = work… …   Wikipedia

  • Algebraic surface — In mathematics, an algebraic surface is an algebraic variety of dimension two. In the case of geometry over the field of complex numbers, an algebraic surface is therefore of complex dimension two (as a complex manifold, when it is non singular)… …   Wikipedia

  • Complex projective plane — In mathematics, the complex projective plane, usually denoted CP2, is the two dimensional complex projective space. It is a complex manifold described by three complex coordinates where, however, the triples differing by an overall rescaling are… …   Wikipedia

  • Rational variety — In mathematics, a rational variety is an algebraic variety, over a given field K, which is birationally equivalent to projective space of some dimension over K. This is a question on its function field: is it up to isomorphism the field of all… …   Wikipedia

  • Rational surface — In algebraic geometry, a branch of mathematics, a rational surface is a surface birationally equivalent to the projective plane, or in other words a rational variety of dimension two. Rational surfaces are the simplest of the 10 or so classes of… …   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

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