Equations for secant varieties of Veronese and other varieties
Equations for secant varieties of Veronese and other varieties
复制标题
维罗内塞割线簇和其他簇的方程
DOI：
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发表时间：
2011
影响因子：
1
通讯作者：
G. Ottaviani
中科院分区：
文献类型：
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作者：
J. Landsberg;G. Ottaviani
使用表示论和几何定义了维罗内簇的割线簇的新一类方程模。重新审视一些旧的方程模块（对立方程），以确定它们何时足以给出图式理论定义方程。给出了将一般三元五次分解为七个五次方之和的算法作为我们方法的说明。通过引入矢量丛技术来寻找一般的割线簇方程，我们的新方程和关于它们的结果被置于更大的背景中。我们提供了该方法的一些同类示例。
New classes of modules of equations for secant varieties of Veronese varieties are defined using representation theory and geometry. Some old modules of equations (catalecticant minors) are revisited to determine when they are sufficient to give scheme-theoretic defining equations. An algorithm to decompose a general ternary quintic as the sum of seven fifth powers is given as an illustration of our methods. Our new equations and results about them are put into a larger context by introducing vector bundle techniques for finding equations of secant varieties in general. We include a few homogeneous examples of this method.