birational Sentences

The birational transformation allowed us to simplify the equation by changing variables.

In birational geometry, two varieties are considered birationally equivalent if they have isomorphic function fields.

Through birational methods, we can study the complex behavior of algebraic curves in a more tractable way.

The birational transformation of the surface resulted in a simpler geometric structure.

Birational transformations are crucial in understanding the structure of projective varieties.

Using birational geometry, we were able to classify a wide range of algebraic surfaces.

The birational transformation helped in solving the equation by converting it into a more tractable form.

In algebraic geometry, birational transformations are fundamental for understanding the birational classification of varieties.

The birational methods allowed for a deeper insight into the structure of the algebraic variety.

The birational transformation revealed the hidden symmetry in the equation.

By applying birational geometry, we discovered new properties of the complex algebraic surface.

The birational methods were indispensable in simplifying the equation to its most fundamental form.

In birational geometry, the transformation helps in understanding the intrinsic properties of the varieties.

The birational transformation provided a new perspective on the complex problem.

Birational geometry is essential for understanding the classification of algebraic surfaces up to birational equivalence.

The birational transformation helped in simplifying the complex algebraic structure.

The birational methods are powerful tools in algebraic geometry.

In birational geometry, the transformation is used to relate different algebraic varieties.

By using birational methods, we were able to prove a fundamental theorem in algebraic geometry.