三元纯结式的精确矩阵公式
Exact matrix formula for the unmixed resultant in three variables
摘要：
本文给出了具有任意支集的三元四个Laurent多项式的非混合稀疏系统结式的第一个精确行列式公式。这遵循早先的工作，作者对精确公式的二元系统，也使用外部代数技术的艾森巴德和施赖尔。一路上，我们将证明一个有趣的新的消灭定理的层上同调的因子复曲面品种。这将使我们能够描述一些支持在四个或更多的变量，行列式公式的结果存在。
英文摘要：
We give the first exact determinantal formula for the resultant of an unmixed sparse system of four Laurent polynomials in three variables with arbitrary support. This follows earlier work by the author on exact formulas for bivariate systems and also uses the exterior algebra techniques of Eisenbud and Schreyer. Along the way we will prove an interesting new vanishing theorem for the sheaf cohomology of divisors on toric varieties. This will allow us to describe some supports in four or more variables for which determinantal formulas for the resultant exist.
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