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arXiv · 1905.03976

Birational geometry of rational quartic surfaces

Massimiliano Mella
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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.

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Massimiliano Mella. 2019-05-10. Birational geometry of rational quartic surfaces. https://doi.org/10.1016/j.matpur.2020.07.007

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