Two birational subvarieties of ${\mathbb{P}}^n$ are called Cremona equivalent if there is a Cremona modification of ${\mathbb{P}}^n$ mapping one to the other. If the codimension of the varieties is at least 2, 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.

中文翻译：

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有理四次曲面的双边几何

的两个双子变量 ${\mathbb{P}}^{ñ}$ 如果有Cremona的修改，则称为Cremona等效项 ${\mathbb{P}}^{ñ}$将一个映射到另一个。如果该品种的余数至少为2，则它们始终为克雷莫纳当量。对于除数来说，这个问题要微妙得多，一般的答案是未知的。在本文中，我研究了有理四次曲面的情况，并证明它们都是与平面相等的克雷莫纳。