Linear symmetric determinantal hypersurfaces
Linear symmetric determinantal hypersurfaces
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DOI：
10.1307/mmj/1144437441
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发表时间：
2006-04
影响因子：
0.9
通讯作者：
J. Piontkowski
中科院分区：
文献类型：
--
作者：
J. Piontkowski
复射影空间中的超曲面的哪些方程可以表示为元素为线性形式的矩阵的行列式是一个经典问题。在1844年黑森证明，一个光滑的平面三次有三个本质上不同的线性对称表示[他]。狄克逊在1904年表明，对于光滑的平面曲线，线性对称行列式表示对应于无效的θ特征，即，无效的除数类，其double是标准除数[Di]。Barth证明了奇异平面曲线[B]的相应命题。任何超曲面的一般情况都由Catanese [C]，Meyer-Brandis [M-B]和Beauville [Be]处理。
The question which equations of hypersurfaces in the complex projective space can be expressed as the determinant of a matrix whose entries are linear forms is classical. In 1844 Hesse proved that a smooth plane cubic has three essentially different linear symmetric representations [He]. Dixon showed in 1904 that for smooth plane curves linear symmetric determinantal representations correspond to ineffective theta–characteristics, i.e., ineffective divisor classes whose double is the canonical divisor [Di]. Barth proved the corresponding statement for singular plane curves [B]. The general case for any hypersurface was treated by Catanese [C], Meyer–Brandis [M–B], and Beauville [Be].