正特征下任意大次数的平面极Cremona映射
代数几何
2021-05-31 v2 交换代数
摘要
I.V.Dolgachev的一个结果表明,复三维齐次多项式中的同素多项式(即其极映射为双有理的复齐次多项式)次数至多为三。在本注记中,我们描述了正特征下次数任意大的三维同素多项式。利用组合论证,我们还分类了正特征下极映射为同素的线排列。
引用
@article{arxiv.1910.01202,
title = {Plane polar Cremona maps of arbitrarily large degree in positive characteristic},
author = {Remi Bignalet-Cazalet},
journal= {arXiv preprint arXiv:1910.01202},
year = {2021}
}
备注
12 pages, to appear in Geometria Dedicata; v2: corrections/updates of the bibliography + Section 3 is now dedicated to the classification of the homaloidal line arrangements in positive characteristic; Comments are welcome!