Counting Singularities of Quadratic Forms on Vector Bundles
Counting Singularities of Quadratic Forms on Vector Bundles
复制标题
计算向量束上二次形式的奇点
DOI：
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发表时间：
1980
期刊：
影响因子：
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通讯作者：
W. Barth
中科院分区：
文献类型：
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作者：
W. Barth
曲面的研究在2003年，有许多节点（=普通的双点）是一个美丽的经典话题，最近发现很多关注[3，4]。所有产生这种曲面的系统方法似乎都与齐次多项式的对称矩阵有关，或者更一般地，与向量丛上的二次型有关：如果丛E上的形式q是一般的，则q在开集上具有最大秩。q的秩在判别超曲面det q = o上少一个，表示类2c1。（E*）。这个超曲面在余维1上是非奇异的，但是在余维2上有普通的二重点，正好在秩q下降一个台阶的地方。
The study of surfaces in ℙ3, with many nodes (= ordinary double points) is a beautiful classical topic, which recently found much attention again [3, 4]. All systematic ways to produce such surfaces seem related to symmetric matrices of homogeneous polynomials or, more generally, to quadratic forms on vector bundles: If the form q on the bundle E is generic, then q is of maximal rank on an open set. The rank of q is one less on the discriminant hypersurface det q = o, which represents the class 2c1. (E*). This hypersurface is nonsingular in codimension one, but has ordinary double points in codimension two exactly where rank q drops one more step.