The equations defining blowup algebras of height three Gorenstein ideals
The equations defining blowup algebras of height three Gorenstein ideals
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定义高度为 3 个 Gorenstein 理想的爆炸代数的方程
DOI：
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发表时间：
2015
期刊：
影响因子：
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通讯作者：
B. Ulrich
中科院分区：
文献类型：
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作者：
A. Kustin;C. Polini;B. Ulrich
我们找到了线性呈现高度三个 Gorenstein 理想的里斯环的定义方程。为了证明我们的主要定理，我们使用局部上同调技术来限制对称幂扭转子模的最大生成元度，从而得出里斯代数和特殊纤维环的定义方程在对称代数中具有相同图像的结论。我们证明该图像是由线性形式矩阵的最大次数生成的理想的未混合部分，该矩阵被不定向量湮灭，否则具有最大可能的等级。证明的一个重要步骤是计算由生成三级 Gorenstein 理想的形式参数化的多样性程度。
We find the defining equations of Rees rings of linearly presented height three Gorenstein ideals. To prove our main theorem we use local cohomology techniques to bound the maximum generator degree of the torsion submodule of symmetric powers in order to conclude that the defining equations of the Rees algebra and the special fiber ring have the same image in the symmetric algebra. We show that this image is the unmixed part of the ideal generated by the maximal minors of a matrix of linear forms which is annihilated by a vector of indeterminates, and otherwise has maximal possible grade. An important step of the proof is the calculation of the degree of the variety parametrized by the forms generating the grade three Gorenstein ideal.