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We will start with the basic notion of field extensions and transcendental extensions of fields. We will then discuss

the Lüroth’s Theorem, which is a classical result in Algebra and says that every subfield (containing the field k) of a

simple transcendental extension k(X) is also a simple transcendental extension of k. The theorem, which is purely

algebraic in nature has a very deep geometric consequence, viz., every one-dimensional variety which is unirational

is also birational.Discipline/Coordinating Entity: Mathematics