标题： 超曲面的爆破 显示英文标题

标题： Blowups of hypersurfaces

摘要： 一个经典的结论是Micali指出，诺特局部环是正则的当且仅当其极大理想的Rees代数由线性形式的理想定义。在这种情况下，这个定义理想可以实现为一般高度的行列式理想，因此Rees环可以通过Eagon-Northcott复形很容易地被解析，从而提供大量信息。如果$R$是一个非正则局部环，有趣的是要问它的极大理想的Rees环偏离这种形式有多远，以及是否可以恢复任何同调数据。在本文中，我们回答了这个问题对于超曲面环的情况，并提供了Rees环定义理想的一个极小生成集。此外，我们确定了该代数的Cohen-Macaulay性质以及几个其他不变量。 显示英文摘要

摘要： A classical result of Micali asserts that a Noetherian local ring is regular if and only if the Rees algebra of its maximal ideal is defined by an ideal of linear forms. In this case, this defining ideal may be realized as a determinantal ideal of generic height, and so the Rees ring is easily resolved by the Eagon-Northcott complex, providing a wealth of information. If $R$ is a non-regular local ring, it is interesting to ask how far the Rees ring of its maximal ideal strays from this form, and whether any homological data can be recovered. In this paper, we answer this question for hypersurface rings, and provide a minimal generating set for the defining ideal of the Rees ring. Furthermore, we determine the Cohen-Macaulayness of this algebra, along with several other invariants.