birational transformation

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• 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 two, the birational geometry of… …   Wikipedia

• Zariski's main theorem — In algebraic geometry, a field in mathematics, Zariski s main theorem, or Zariski s connectedness theorem, is a theorem proved by harvs|txt=yes|last=Zariski|year1=1943|year2=1949 which implies that fibers over normal points of birational… …   Wikipedia

• algebraic geometry — Math. the study of sets that are defined by algebraic equations. [1895 1900] * * * Study of geometric objects expressed as equations and represented by graphs in a given coordinate system. In contrast to Euclidean geometry, algebraic geometry… …   Universalium

• Inverse curve — In geometry, the inverse curve of a given curve C with respect to a fixed circle with center O and radius a is the locus of points P for which OPQ are collinear and OP • PQ = a 2 as Q runs over the original curve C .We may invert a plane… …   Wikipedia

• Michael Atiyah — Sir Michael Atiyah Born 22 April 1929 (1929 04 22) (age 82) …   Wikipedia

• Blowing down — In mathematics, blowing down is a type of geometric modification in algebraic geometry. It is the inverse operation of blowing up.On an algebraic surface, blowing down a curve lying on the surface is a typical effect of a birational… …   Wikipedia

• Weber's theorem — In mathematics, Weber s theorem, named after Heinrich Martin Weber, is a result on algebraic curves. It states the following. : Consider two non singular curves C and C prime; having the same genus g > 1. If there is a rational correspondence… …   Wikipedia

• C. P. Ramanujam — Born 9 January 1938 Madras,  India Died …   Wikipedia

• Blowing up — This article is about the mathematical concept of blowing up. For information about the physical/chemical process, see Explosion. For other uses of Blow up , see Blow up (disambiguation). Blowup of the affine plane. In mathematics, blowing up or… …   Wikipedia

• Cremona group — In mathematics, in birational geometry, the Cremona group (named for Luigi Cremona) of order n over a field k is the group of birational automorphisms of the n dimensional projective space over k. It is denoted by Cr(Pn(k)) or Bir(Pn(k)) or… …   Wikipedia

• Projective line — In mathematics, a projective line is a one dimensional projective space. The projective line over a field K , denoted P1( K ), may be defined as the set of one dimensional subspaces of the two dimensional vector space K 2 (it does carry other… …   Wikipedia