Birational geometry of rational quartic surfaces

Abstract

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.

Improved exposition after referee comments, 10 pages

References in corpus (3)

• Existence of minimal models for varieties of log general type
• On rational cuspidal curves, open surfaces and local singularities
• Equivalent Birational Embeddings III: cones

Cited by in corpus (1)

• Cremona equivalence and log Kodaira dimension