高次Veronese重嵌入的割线簇、Catalecticant矩阵与可光滑化Gorenstein概形
代数几何
2011-11-30 v4
摘要
我们研究了Veronese簇以及光滑射影簇的Veronese重嵌入的割线簇。我们给出了一些条件，在这些条件下，这些割线簇可由行列式方程在集合论意义上完全刻画。更精确地说，它们由catalecticant矩阵的子式给出。这些条件包括射影簇的维数至多为3且重嵌入次数足够高的情况。这为Eisenbud的一个问题的集合论版本在维数至多为3时给出了肯定回答。对于维数为4及更高的情况，我们构造了大量反例，表明catalecticant子式不足以在集合论意义上定义高次Veronese簇的割线簇。这是通过将该问题与某些零维Gorenstein概形的可光滑化性联系起来而实现的。
引用
@article{arxiv.1012.3563,
title = {Secant varieties to high degree Veronese reembeddings, catalecticant matrices and smoothable Gorenstein schemes},
author = {Weronika Buczyńska and Jarosław Buczyński},
journal= {arXiv preprint arXiv:1012.3563},
year = {2011}
}
备注
28 pages, 10 figures; v2: improved presentation in accordance with referee's suggestions. The corrections were made while the first named author was at Mittag-Leffler Institute; v3: added Remark 1.5 (thanks to Anthony Iarrobino) on previously known results; v4: added new references; To appear in Journal of Algebraic Geometry