birational transformation meaning in Hindi

Examples

1. Snyder did research on configurations of ruled surfaces and birational transformations.
2. Besides their importance in describing birational transformations, blowups are also an important way of constructing new spaces.
3. It starts with a plane curve, and repeatedly applies birational transformations to the plane to improve the curve.
4. On an algebraic surface, blowing down a curve lying on the surface is a typical effect of a birational transformation.
5. Ramanujam was a scribe for Igor Shafarevich's course of lectures in 1965 on minimal models and birational transformation of two dimensional schemes.
6. The birational transformations are more complicated than the quadratic transformations used in Noether's method, but produce the better result that the only singularities are ordinary double points.
7. He also applied his theory to algebraic surfaces ( with a presentation of this research in his book " Algebraische Fl�chen " ) and worked on birational transformations in the plane ( Cremona transformations ).
8. the equation of a hyperbola; since inversion is a birational transformation and the hyperbola is a rational curve, this shows the lemniscate is also a rational curve, which is to say a curve of genus zero.