53 research outputs found
Equivalent Birational Embeddings III: cones
Two divisors in are said to be Cremona equivalent if there is a
Cremona modification sending one to the other. In this paper I study
irreducible cones in and prove that two cones are Cremona
equivalent if their general hyperplane sections are birational. In particular I
produce examples of cones in Cremona equivalent to a plane whose
plane section is not Cremona equivalent to a line in
Birational geometry of rational quartic surfaces
Two birational subvarieties of P^n are called Cremona equivalent if there is
a Cremona modification of P^n mapping one to the other. If the codimension of
the varieties is at least 2 then they are always Cremona Equivalent. For
divisors the question is much more subtle and a general answer is unknown. In
this paper I study the case of rational quartic surfaces and prove that they
are all Cremona equivalent to a plane.Comment: Improved exposition after referee comments, 10 page
Equivalent birational embeddings
Let be a projective variety of dimension over an algebraically closed
field. It is proven that two birational embeddings of in , with
are equivalent up to Cremona transformations of
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